{"id":55,"date":"2021-05-19T17:06:42","date_gmt":"2021-05-19T17:06:42","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/basicreview\/chapter\/whole-numbers\/"},"modified":"2023-08-08T20:38:14","modified_gmt":"2023-08-08T20:38:14","slug":"whole-numbers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/basicreview\/chapter\/whole-numbers\/","title":{"raw":"1.1 Whole Numbers","rendered":"1.1 Whole Numbers"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Use place value with whole numbers<\/li>\r\n \t<li>Identify multiples and apply divisibility tests<\/li>\r\n \t<li>Find prime factorization and least common multiples<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655154091\">As we begin our study of intermediate algebra, we need to refresh some of our skills and vocabulary. This chapter and the next will focus on whole numbers, integers, fractions, decimals, and real numbers. We will also begin our use of algebraic notation and vocabulary.<\/p>\r\n\r\n<h1>Use Place Value with Whole Numbers<\/h1>\r\n<p id=\"fs-id1170655162029\">The most basic numbers used in algebra are the numbers we use to count objects in our world: 1, 2, 3, 4, and so on. These are called the counting number<strong data-effect=\"bold\">s<\/strong>. Counting numbers are also called <em data-effect=\"italics\">natural numbers<\/em>. If we add zero to the counting numbers, we get the set of whole number<strong data-effect=\"bold\">s<\/strong>.<\/p>\r\n<p id=\"fs-id1170655024948\">\\(\\phantom{\\rule{1.5em}{0ex}}\\)Counting Numbers: 1, 2, 3, \u2026<\/p>\r\n<p id=\"fs-id1170655082425\">\\(\\phantom{\\rule{1.5em}{0ex}}\\)Whole Numbers: 0, 1, 2, 3, \u2026<\/p>\r\n<p id=\"fs-id1170655192198\">The notation \u201c\u2026\u201d is called ellipsis and means \u201cand so on,\u201d or that the pattern continues endlessly.<\/p>\r\n<p id=\"fs-id1170655197123\">We can visualize counting numbers and whole numbers on a number line .See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_001_new\">Figure 1<\/a>.<\/p>\r\n\r\n<div id=\"CNX_ElemAlg_Figure_01_01_001_new\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left. While this number line shows only the whole numbers 0 through 6, the numbers keep going without end.<\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"750\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/05\/CNX_ElemAlg_Figure_01_01_001_new.jpg\" alt=\"A horizontal number line with arrows on each end and values of zero to six runs along the bottom of the diagram. A second horizontal line with a left-facing arrow lies above the first and extend from zero to three. This line is labled \u201csmaller\u201d. A third horizontal line with a right-facing arrow lies above the first two, but runs from three to six and is labeled \u201clarger\u201d.\" width=\"750\" height=\"117\" data-media-type=\"image\/jpeg\" \/> Figure 1[\/caption]\r\n\r\n<\/div>\r\n<p id=\"fs-id1170655190408\">Our <span class=\"no-emphasis\" data-type=\"term\">number system<\/span> is called a place value system, because the value of a digit depends on its position in a number. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_002_new\">Figure 2<\/a> shows the <span class=\"no-emphasis\" data-type=\"term\">place values<\/span>. The place values are separated into groups of three, which are called periods. The periods are <em data-effect=\"italics\">ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.<\/p>\r\nThe number 5,278,194 is shown in the chart. The digit 5 is in the millions place. The digit 2 is in the hundred-thousands place. The digit 7 is in the ten-thousands place. The digit 8 is in the thousands place. The digit 1 is in the hundreds place. The digit 9 is in the tens place. The digit 4 is in the ones place.\r\n<div id=\"CNX_ElemAlg_Figure_01_01_002_new\" class=\"bc-figure figure\">\r\n<div><\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"377\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_002_new.jpg\" alt=\"This figure is a table illustrating the number 5,278,194 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 5, 2, 7, 8, 1, 9, 4. This means there are 5 millions, 2 hundred thousands, 7 ten thousands, 8 thousands, 1 hundreds, 9 tens, and 4 ones in the number five million two hundred seventy-nine thousand one hundred ninety-four.\" width=\"377\" height=\"289\" data-media-type=\"image\/jpeg\" \/> Figure 2[\/caption]\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654978132\" data-type=\"problem\">\r\n<p id=\"fs-id1170655192807\">In the number 63,407,218, find the place value of each digit:<\/p>\r\n\r\n<ol id=\"fs-id1166421427575\" class=\"circled\" type=\"a\">\r\n \t<li>7<\/li>\r\n \t<li>0<\/li>\r\n \t<li>1<\/li>\r\n \t<li>6<\/li>\r\n \t<li>3<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1170655022351\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654968077\">Place the number in the place value chart:<\/p>\r\n<span id=\"fs-id1170655112880\" data-type=\"media\" data-alt=\"This figure is a table illustrating the number 63,407,218 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cTen millions\u201d, \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 6, 3, 4, 0, 7, 2, 1, 8. This means there are 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, and 8 ones in the number sixty-three million, four hundred seven thousand, two hundred eighteen.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_003_img_new.jpg\" alt=\"This figure is a table illustrating the number 63,407,218 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cTen millions\u201d, \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 6, 3, 4, 0, 7, 2, 1, 8. This means there are 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, and 8 ones in the number sixty-three million, four hundred seven thousand, two hundred eighteen.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1166426398759\">a) The 7 is in the thousands place.\r\nb) The 0 is in the ten thousands place.\r\nc) The 1 is in the tens place.\r\nd) The 6 is in the ten-millions place.\r\ne) The 3 is in the millions place.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655125783\" data-type=\"problem\">\r\n<p id=\"fs-id1170655133227\">For the number 27,493,615, find the place value of each digit:<\/p>\r\n<p id=\"fs-id1170655154330\">a) 2\u2003b) 1\u2003c) 4\u2003d) 7\u2003e) 5<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655192955\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654924451\">a) ten millions b) tens c) hundred thousands d) millions e) ones<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655171837\" data-type=\"problem\">\r\n<p id=\"fs-id1170655171777\">For the number 519,711,641,328, find the place value of each digit:<\/p>\r\n<p id=\"fs-id1170655114062\">a) 9\u2003b) 4\u2003c) 2\u2003d) 6\u2003e) 7<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655129771\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655163552\">a) billions b) ten thousands c) tens d) hundred thousands e) hundred millions<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655113270\">When you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period, followed by the name of the period, without the <em data-effect=\"italics\">s<\/em> at the end. Start at the left, where the periods have the largest value. The ones period is not named. The commas separate the periods, so wherever there is a comma in the number, put a comma between the words (see <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_004_new\">Figure 3)<\/a>. The number 74,218,369 is written as seventy-four million, two hundred eighteen thousand, three hundred sixty-nine.<\/p>\r\n\r\n<div id=\"CNX_ElemAlg_Figure_01_01_004_new\" class=\"bc-figure figure\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"503\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_004_new.jpg\" alt=\"In this figure, the numbers 74, 218 and 369 are listed in a row, separated by commas. Each number has a curly bracket beneath it with the word \u201cmillions\u201d written below the number 74, \u201cthousands\u201d written below the number 218, and \u201cones\u201d written below the number 369. A left-facing arrow points at these three words, labeling them \u201cperiods\u201d. One row down is the number \u201c74\u201d, a right-facing arrow and the words \u201cSeventy-four million\u201d followed by a comma. The next row below is the number \u201c218\u201d, a right-facing arrow and the words \u201ctwo hundred eighteen thousand\u201d followed by a comma. On the bottom row is the number \u201c369\u201d, a right-facing arrow and the words \u201cthree hundred sixty-nine\u201d.\" width=\"503\" height=\"137\" data-media-type=\"image\/jpeg\" \/> Figure 3[\/caption]\r\n\r\n<\/div>\r\n<div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Name a Whole Number in Words.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166426255157\" class=\"stepwise\" type=\"1\">\r\n \t<li>Start at the left and name the number in each period, followed by the period name.<\/li>\r\n \t<li>Put commas in the number to separate the periods.<\/li>\r\n \t<li>Do not name the ones period.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655127621\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655175454\" data-type=\"problem\">\r\n<p id=\"fs-id1170654981580\">Name the number 8,165,432,098,710 using words.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654857936\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170655134588\">Name the number in each period, followed by the period name.<\/p>\r\n<span id=\"fs-id1170655155229\" data-type=\"media\" data-alt=\"In this figure, the numbers 8, 165, 432, 098 and 710 are listed in a row, separated by commas. Each number has a horizontal bracket beneath with the word \u201ctrillions\u201d written below the number 8, \u201cbillions\u201d written below the number 165, \u201cmillions\u201d written below the number 432, \u201cthousands\u201d written below the number 098, and \u201cones\u201d written below the number 710. One row down is the number 8, a right-facing arrow and the words \u201cEight trillion\u201d followed by a comma. On the next row below is the number 165, a right-facing arrow and the words \u201cOne hundred sixty-five billion\u201d followed by a comma. On the next row below is the number 432, a right-facing arrow and the words \u201cFour hundred thirty-two million\u201d followed by a comma. On the next row below is the number \u201c098\u201d, a right-facing arrow and the words \u201cNinety-eight thousand\u201d followed by a comma. On the bottom row is the number 710, a right-facing arrow and the words \u201cSeven hundred ten\u201d.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_005_img_new.jpg\" alt=\"In this figure, the numbers 8, 165, 432, 098 and 710 are listed in a row, separated by commas. Each number has a horizontal bracket beneath with the word \u201ctrillions\u201d written below the number 8, \u201cbillions\u201d written below the number 165, \u201cmillions\u201d written below the number 432, \u201cthousands\u201d written below the number 098, and \u201cones\u201d written below the number 710. One row down is the number 8, a right-facing arrow and the words \u201cEight trillion\u201d followed by a comma. On the next row below is the number 165, a right-facing arrow and the words \u201cOne hundred sixty-five billion\u201d followed by a comma. On the next row below is the number 432, a right-facing arrow and the words \u201cFour hundred thirty-two million\u201d followed by a comma. On the next row below is the number \u201c098\u201d, a right-facing arrow and the words \u201cNinety-eight thousand\u201d followed by a comma. On the bottom row is the number 710, a right-facing arrow and the words \u201cSeven hundred ten\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170654915073\">Put the commas in to separate the periods.<\/p>\r\n<p id=\"fs-id1170655164902\">So, \\(8,165,432,098,710\\) is named as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655195315\" data-type=\"problem\">\r\n<p id=\"fs-id1170654905813\">Name the number \\(9,258,137,904,061\\) using words.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655096352\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654989620\">nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655157875\" data-type=\"problem\">\r\n<p id=\"fs-id1170655162513\">Name the number \\(17,864,325,619,004\\) using words.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654977617\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654957397\">seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand, four<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655190403\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655075933\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655195315\" data-type=\"problem\">We are now going to reverse the process by writing the digits from the name of the number. To write the number in digits, we first look for the clue words that indicate the periods. It is helpful to draw three blanks for the needed periods and then fill in the blanks with the numbers, separating the periods with commas.<\/div>\r\n<div data-type=\"problem\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Write a Whole Number Using Digits.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166426255684\" class=\"stepwise\" type=\"1\">\r\n \t<li>Identify the words that indicate periods. (Remember, the ones period is never named.)<\/li>\r\n \t<li>Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\r\n \t<li>Name the number in each period and place the digits in the correct place value position.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655200529\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654859177\" data-type=\"problem\">\r\n<p id=\"fs-id1170655025082\">Write <em data-effect=\"italics\">nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine<\/em> as a whole number using digits.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655120857\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170655190501\">Identify the words that indicate periods.\r\nExcept for the first period, all other periods must have three places. Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.\r\nThen write the digits in each period.<\/p>\r\n<span id=\"fs-id1170655154739\" data-type=\"media\" data-alt=\"An image has two lines of text. The upper lines read \u201cnine billion\u201d, followed by a comma, and \u201ctwo hundred forty six million\u201d, also followed by a comma. The words \u201cbillion\u201d and \u201cmillion\u201d are underlined and each phrase has a curly bracket underneath. The lower lines read \u201cseventy three thousand\u201d, followed by a comma, and \u201cone hundred eighty nine\u201d. The word \u201cthousand\u201d is underlined and each phrase has a curly bracket underneath.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_022_img_new.jpg\" alt=\"An image has two lines of text. The upper lines read \u201cnine billion\u201d, followed by a comma, and \u201ctwo hundred forty six million\u201d, also followed by a comma. The words \u201cbillion\u201d and \u201cmillion\u201d are underlined and each phrase has a curly bracket underneath. The lower lines read \u201cseventy three thousand\u201d, followed by a comma, and \u201cone hundred eighty nine\u201d. The word \u201cthousand\u201d is underlined and each phrase has a curly bracket underneath.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\nThe number is 9,246,073,189.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655160983\" data-type=\"problem\">\r\n<p id=\"fs-id1170655162842\">Write the number two billion, four hundred sixty-six million, seven hundred fourteen thousand, fifty-one as a whole number using digits.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655025046\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655160558\">\\(2,466,714,051\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655025845\" data-type=\"problem\">\r\n<p id=\"fs-id1170655155164\">Write the number eleven billion, nine hundred twenty-one million, eight hundred thirty thousand, one hundred six as a whole number using digits.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654964907\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654982481\">\\(11,921,830,106\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nIn 2016, Statistics Canada estimated the population of Toronto as 13,448,494. We could say the population of Toronto was approximately 13.4 million. In many cases, you don\u2019t need the exact value; an approximate number is good enough.\r\n<p id=\"fs-id1170655007229\">The process of approximating a number is called <span class=\"no-emphasis\" data-type=\"term\">rounding<\/span>. Numbers are rounded to a specific place value, depending on how much accuracy is needed. Saying that the population of Toronto is approximately 13.4 million means that we rounded to the hundred thousands place.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655027531\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655120684\" data-type=\"problem\">\r\n<p id=\"fs-id1170655105094\">Round 23,658 to the nearest hundred.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655134210\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1170655194626\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains the numbers corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Locate the given place value with an arrow. All digits to the left do not change.\u201d In the the second cell, the instructions say: \u201cLocate the hundreds place in 23,658.\u201d In the third cell, there is the number 23,658 with an arrow pointing to the digit 6, labeling it \u201chundreds place.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains the numbers corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Locate the given place value with an arrow. All digits to the left do not change.\u201d In the the second cell, the instructions say: \u201cLocate the hundreds place in 23,658.\u201d In the third cell, there is the number 23,658 with an arrow pointing to the digit 6, labeling it \u201chundreds place.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655028499\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. Underline the digit to the right of the given place value.\u201d In the second cell, the instructions say: \u201cUnderline the 5, which is to the right of the hundreds place.\u201d In the third cell, there is the number 23,658 again, the same arrow pointing to the digit 6, labeling it the hundreds place. The 5 is also underlined in this cell.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. Underline the digit to the right of the given place value.\u201d In the second cell, the instructions say: \u201cUnderline the 5, which is to the right of the hundreds place.\u201d In the third cell, there is the number 23,658 again, the same arrow pointing to the digit 6, labeling it the hundreds place. The 5 is also underlined in this cell.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654984954\" data-type=\"media\" data-alt=\"One row down, the first cell says: \u201cStep 3. Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do not change the digit in the given place value.\u201d In the second cell, the instructions say: \u201cAdd 1 to the 6 in the hundreds place, since 5 is greater than or equal to 5.\u201d The third cell contains the number 23,658 again, with an arrow pointing at the digit 6 and the text \u201cadd 1\u201d. There is also a curly bracket under the digits 5 and 8, with an arrow pointing at them and the text \u201creplace with 0s.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008c_new.jpg\" alt=\"One row down, the first cell says: \u201cStep 3. Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do not change the digit in the given place value.\u201d In the second cell, the instructions say: \u201cAdd 1 to the 6 in the hundreds place, since 5 is greater than or equal to 5.\u201d The third cell contains the number 23,658 again, with an arrow pointing at the digit 6 and the text \u201cadd 1\u201d. There is also a curly bracket under the digits 5 and 8, with an arrow pointing at them and the text \u201creplace with 0s.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655130142\" data-type=\"media\" data-alt=\"In the bottom row, the first cell says: \u201cStep 4. Replace all digits to the right of the given place value with zeros. So, 23,700 is rounded to the nearest hundred.\u201d In the second cell, the instructions say: \u201cReplace all digits to the right of the hundreds place with zeros.\u201d The third cell contains the number 23,700, which we have reached by rounding the number 23,658 to the nearest hundred.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008d_new.jpg\" alt=\"In the bottom row, the first cell says: \u201cStep 4. Replace all digits to the right of the given place value with zeros. So, 23,700 is rounded to the nearest hundred.\u201d In the second cell, the instructions say: \u201cReplace all digits to the right of the hundreds place with zeros.\u201d The third cell contains the number 23,700, which we have reached by rounding the number 23,658 to the nearest hundred.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655171044\" data-type=\"problem\">\r\n<p id=\"fs-id1170655128617\">Round to the nearest hundred: \\(17,852\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654925300\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655108383\">\\(17,900\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655202716\" data-type=\"problem\">\r\n<p id=\"fs-id1170655166306\">Round to the nearest hundred: \\(468,751\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654893026\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654863185\">\\(468,800\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Round Whole Numbers.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166426178564\" class=\"stepwise\" type=\"1\">\r\n \t<li>Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.<\/li>\r\n \t<li>Underline the digit to the right of the given place value.<\/li>\r\n \t<li>Is this digit greater than or equal to 5?\r\n<ul id=\"fs-id1170654989989\" data-bullet-style=\"bullet\">\r\n \t<li>Yes\u2013add \\(1\\) to the digit in the given place value.<\/li>\r\n \t<li>No\u2013do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Replace all digits to the right of the given place value with zeros.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655190444\" class=\"howto\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655166809\" data-type=\"problem\">\r\n<p id=\"fs-id1170655151020\">Round \\(103,978\\) to the nearest:<\/p>\r\n\r\n<ol id=\"fs-id1166426039326\" class=\"circled\" type=\"a\">\r\n \t<li>hundred<\/li>\r\n \t<li>thousand<\/li>\r\n \t<li>ten thousand<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1170655106038\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1167835319528\">a)<\/p>\r\n\r\n<table id=\"fs-id1167832055010\" class=\"unnumbered unstyled\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the hundreds place in 103,978.\u201d On the right are the words \u201chundreds place\u201d, followed by an arrow pointing down at the digit 9 in the number 103,978. One row down, the instructions on the left say \u201cUnderline the digit to the right of the hundreds place\u201d. On the right are the words \u201chundreds place\u201d again followed by the same arrow pointing at the digit 9 in 103,978, but the number 7 is also underlined. One row down, the instructions on the left say \u201cSince 7 is greater than or equal to 5, add 1 to the 9. Replace all digits to the right of the hundreds place with zeros.\u201d On the right, the number 103,978 is repeated with the 3 still labeled with the text \u201chundreds place\u201d and the 7 underlined. Another arrow points to the 3 with the text \u201cadd 1; 9 plus 1 equals 10; replace 9 with 0 and carry the 1\u201d. A bracket is drawn underneath the underlined 7 and an arrow points at this bracket with the text \u201creplace with 0s\u201d. One row down, the number 104,000 appears on the right. At the bottom of the image, the text on the left says \u201cSo, 104,000 is 103,978 rounded to the nearest hundred.\u201d\" width=\"100%\">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Locate the hundreds place in 103,978.<\/td>\r\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167831970141\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Underline the digit to the right of the hundreds place.<\/td>\r\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167834196335\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Since 7 is greater than or equal to 5, add 1 to the 9. Replace all digits to the right of the hundreds place with zeros.<\/td>\r\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167831823617\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><\/td>\r\n<td data-valign=\"top\" data-align=\"left\">So, 104,000 is 103,978 rounded to the nearest hundred.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1167831894747\">b)<\/p>\r\n\r\n<table id=\"fs-id1167834184013\" class=\"unnumbered unstyled can-break\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the thousands place and underline the digit to the right of the thousands place.\u201d On the right are the words \u201cthousands place\u201d, followed by an arrow pointing down at the digit 3 in the number 103,978. The digit 9 is underlined. One row down, the instructions on the left say \u201cSince 9 is greater than or equal to 5 add 1 to the 3. Replace all digits to the right of the hundreds place with zeros.\u201d On the right, the number 103,978 is repeated with the 3 still labeled with the text \u201cthousands place\u201d and the 9 underlined. Another arrow points to the 3 with the text \u201cadd 1; 3 plus 1 equals 4; replace 3 with 4\u201d. A bracket is drawn underneath the last three digits, 978, and an arrow points at this bracket with the text \u201creplace with 0s\u201d. One row down, the number 104,000 appears on the right. At the bottom of the image, the text on the left says \u201cSo, 104,000 is 103,978 rounded to the nearest thousand.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Locate the thousands place and underline the digit to the right of the thousands place.<\/td>\r\n<td><span id=\"fs-id1167835305151\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since 9 is greater than or equal to 5, add 1 to the 3. Replace all digits to the right of the hundreds place with zeros.<\/td>\r\n<td><span id=\"fs-id1167834132960\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>So, 104,000 is 103,978 rounded to the nearest thousand.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1167832134211\">c)<\/p>\r\n\r\n<table id=\"fs-id1167832006514\" class=\"unnumbered unstyled\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the ten thousands place and underline the digit to the right of the ten thousands place.\u201d On the right are the words \u201cten thousands place\u201d, followed by an arrow pointing down at the digit 0 in the number 103,978. The digit 3 is underlined. One row down, the instructions on the left say \u201cSince 0 is less than 5, we leave it as is, and then replace the digits to the right with zeros.\u201d On the right is the number 100,000. At the bottom of the image, the text on the left says \u201cSo, 100,000 is 103,978 rounded to the nearest ten thousand.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Locate the ten thousands place and underline the digit to the right of the ten thousands place.<\/td>\r\n<td>[latex]\\begin{tikzpicture} \\draw[&lt;-,thick] (0,0) -- (0,1); \\node at (0.35,0) [below] {103,978}; \\node at (0,1) [above] {ten thousand's place}; \\end{tikzpicture} [\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since 3 is less than 5, we leave the 0 as is, and then replace the digits to the right with zeros.<\/td>\r\n<td>[latex]100,000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\phantom{\\rule{1.5em}{0ex}}\\)So, 100,000 is 103,978 rounded to the nearest ten thousand.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655154035\" data-type=\"problem\">\r\n<p id=\"fs-id1170655154263\">Round 206,981 to the nearest: a) hundred b) thousand c) ten thousand.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655166679\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655074702\">a) 207,000 b) 207,000 c) 210,000<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655104210\" data-type=\"problem\">\r\n<p id=\"fs-id1170655025825\">Round 784,951 to the nearest: a) hundred b) thousand c) ten thousand.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655226376\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655154551\">a) 785,000 b) 785,000 c) 780,000<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Identify Multiples and Apply Divisibility Tests<\/h1>\r\n<p id=\"fs-id1170655126540\">The numbers 2, 4, 6, 8, 10, and 12 are called multiples of 2. A multiple of 2 can be written as the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of a counting number and 2<\/p>\r\n<span id=\"fs-id1170655216065\" data-type=\"media\" data-alt=\"A diagram made up of two rows of numbers. The top row reads \u201c2, 4, 6, 8, 10, 12,\u201d followed by an elipsis. Below 2 is 2 times 1, below 4 is 2 times 2, below 6 is 2 times 3, below 8 is 2 times 4, below 10 is 2 times 5, and below 12 is 2 times 6.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_012_img_new.jpg\" alt=\"A diagram made up of two rows of numbers. The top row reads \u201c2, 4, 6, 8, 10, 12,\u201d followed by an elipsis. Below 2 is 2 times 1, below 4 is 2 times 2, below 6 is 2 times 3, below 8 is 2 times 4, below 10 is 2 times 5, and below 12 is 2 times 6.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170655163014\">Similarly, a multiple of 3 would be the product of a counting number and 3<\/p>\r\n<span id=\"fs-id1170654944087\" data-type=\"media\" data-alt=\"A diagram made up of two rows of numbers. The top row reads \u201c3, 6, 9, 12, 15, 18,\u201d followed by an elipsis. Below 3 is 3 times 1, below 6 is 3 times 2, below 9 is 3 times 3, below 12 is 3 times 4, below 15 is 3 times 5, and below 18 is 3 times 6.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_013_img_new.jpg\" alt=\"A diagram made up of two rows of numbers. The top row reads \u201c3, 6, 9, 12, 15, 18,\u201d followed by an elipsis. Below 3 is 3 times 1, below 6 is 3 times 2, below 9 is 3 times 3, below 12 is 3 times 4, below 15 is 3 times 5, and below 18 is 3 times 6.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170655150368\">We could find the multiples of any number by continuing this process.<\/p>\r\n<p id=\"fs-id1170654984223\">The <a href=\"#fs-id1170654982162\">Table 1<\/a> below shows the multiples of 2 through 9 for the first 12 counting numbers.<\/p>\r\n\r\n<table id=\"fs-id1170654982162\" class=\"grid\" style=\"height: 176px;width: 100%\" summary=\"This table has ten rows and thirteen columns. In the first row, which is a header row, the cells read left to right \u201cCounting Number\u201d, \u201c1\u201d, \u201c2\u201d, \u201c3\u201d, \u201c4\u201d, \u201c5\u201d, \u201c6\u201d, \u201c7\u201d, \u201c8\u201d, \u201c9\u201d, \u201c10\u201d, \u201c11\u201d, and \u201c12\u201d. In the second row, the cells read left to right \u201cMultiples of 2\u201d, \u201c2\u201d, \u201c4\u201d, \u201c6\u201d, \u201c8\u201d, \u201c10\u201d, \u201c12\u201d, \u201c14\u201d, \u201c16\u201d, \u201c18\u201d, \u201c20\u201d, \u201c22\u201d, and \u201c24\u201d. In the third row, the cells read left to right, \u201cMultiples of 3\u201d, \u201c3\u201d, \u201c6\u201d, \u201c9\u201d, \u201c12\u201d, \u201c15\u201d, \u201c18\u201d, \u201c21\u201d, \u201c24\u201d, \u201c27\u201d, \u201c30\u201d, \u201c33\u201d, and \u201c36\u201d. In the fourth row, the cells read left to right \u201cMultiples of 4\u201d, \u201c4\u201d, \u201c8\u201d, \u201c12\u201d, \u201c16\u201d, \u201c20\u201d, \u201c24\u201d, \u201c28\u201d, \u201c32\u201d, \u201c36\u201d, \u201c40\u201d, \u201c44\u201d, and \u201c48\u201d. In the fifth row, the cells read left to right \u201cMultiples of 5\u201d, \u201c5\u201d, \u201c10\u201d, \u201c15\u201d, \u201c20\u201d, \u201c25\u201d, \u201c30\u201d, \u201c35\u201d, \u201c40\u201d, \u201c45\u201d, \u201c50\u201d, \u201c55\u201d, and \u201c60\u201d. In the sixth row, the cells read left to right \u201cMultiples of 6\u201d, \u201c6\u201d, \u201c12\u201d, \u201c18\u201d, \u201c24\u201d, \u201c30\u201d,\u201d \u201c36\u201d, \u201c\u201d42\u201d, \u201c48\u201d, \u201c54\u201d, \u201c60\u201d, \u201c66\u201d, and \u201c72\u201d. In the seventh row, the cells read left to right \u201cMultiples of 7\u201d, \u201c7\u201d, \u201c14\u201d, \u201c21\u201d, \u201c28\u201d, \u201c35\u201d, \u201c42\u201d, \u201c49\u201d, \u201c56\u201d, \u201c63\u201d, \u201c70\u201d, \u201c77\u201d, and \u201c84\u201d. In the eighth row, the cells read left to right, \u201cMultiples of 8\u201d, \u201c8\u201d, \u201c16\u201d, \u201c24\u201d, \u201c32\u201d, \u201c40\u201d, \u201c48\u201d, \u201c56\u201d, \u201c64\u201d, \u201c72\u201d, \u201c80\u201d, \u201c88\u201d, and \u201c96\u201d. In the ninth row, the cells read left to right \u201cMultiples of 9\u201d, \u201c9\u201d, \u201c18\u201d, \u201c27\u201d, \u201c36\u201d, \u201c45\u201d, \u201c54\u201d, \u201c63\u201d, \u201c72\u201d, \u201c81\u201d, \u201c90\u201d, \u201c99\u201d, and \u201c108\u201d. In the tenth row, the cells read left to right \u201cMultiples of 10\u201d, \u201c10\u201d, \u201c20\u201d, \u201c30\u201d, \u201c40\u201d, \u201c50\u201d, \u201c60\u201d, \u201c70\u201d, \u201c80\u201d, \u201c90\u201d, \u201c100\u201d, \u201c110\u201d, and \u201c120\u201d.\" width=\"100%\"><caption>Table 1<\/caption>\r\n<thead>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<th style=\"height: 16px;width: 67.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">Counting Number<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">1<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">2<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">3<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">4<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">5<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">6<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">7<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">8<\/th>\r\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">9<\/th>\r\n<th style=\"height: 16px;width: 25.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">10<\/th>\r\n<th style=\"height: 16px;width: 24.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">11<\/th>\r\n<th style=\"height: 16px;width: 25.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">12<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 2<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">2<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">4<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">14<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">22<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 3<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">3<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">9<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">15<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">21<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">27<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">33<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 4<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">4<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">28<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">32<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">44<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 5<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">5<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">15<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">25<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">35<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">45<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">50<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">55<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 6<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">42<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">54<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">66<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 7<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">7<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">14<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">21<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">28<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">35<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">42<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">49<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">56<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">63<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">70<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">77<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">84<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 8<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">32<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">56<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">64<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">80<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">88<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">96<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 9<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">9<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">27<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">45<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">54<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">63<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">81<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">90<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">99<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">108<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\" valign=\"top\">\r\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 10<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">50<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">70<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">80<\/td>\r\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">90<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">100<\/td>\r\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">110<\/td>\r\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">120<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170655207886\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\" style=\"text-align: left\">Multiple of a Number<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA number is a <strong data-effect=\"bold\">multiple<\/strong> of <em data-effect=\"italics\">n<\/em> if it is the product of a counting number and <em data-effect=\"italics\">n<\/em>.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655163445\">Another way to say that 15 is a multiple of 3 is to say that 15 is divisible by 3. That means that when we divide 3 into 15, we get a counting number. In fact, \\(15\\div 3\\) is 5, so 15 is \\(5\\cdot 3\\).<\/p>\r\n\r\n<div id=\"fs-id1170655189066\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Divisible by a Number<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf a number <em data-effect=\"italics\">m<\/em> is a multiple of <em data-effect=\"italics\">n<\/em>, then <em data-effect=\"italics\">m<\/em> is <strong data-effect=\"bold\">divisible<\/strong> by <em data-effect=\"italics\">n<\/em>.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655229926\">Look at the multiples of 5 in <a class=\"autogenerated-content\" href=\"#fs-id1170654982162\">Table 1<\/a>. They all end in 5 or 0. Numbers with last digit of 5 or 0 are divisible by 5. Looking for other patterns in <a class=\"autogenerated-content\" href=\"#fs-id1170654982162\">Table 1<\/a> that shows multiples of the numbers 2 through 9, we can discover the following divisibility tests:<\/p>\r\n\r\n<div id=\"fs-id1170655221307\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Divisibility Tests<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1170655202551\">A number is divisible by:<\/p>\r\n\r\n<ul id=\"fs-id1166425936774\" data-bullet-style=\"bullet\">\r\n \t<li>2 if the last digit is 0, 2, 4, 6, or 8.<\/li>\r\n \t<li>3 if the sum of the digits is divisible by 3.<\/li>\r\n \t<li>5 if the last digit is 5 or 0.<\/li>\r\n \t<li>6 if it is divisible by both 2 and 3.<\/li>\r\n \t<li>10 if it ends with 0.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655205194\" data-type=\"problem\">\r\n<p id=\"fs-id1170655205196\">Is 5,625 divisible by 2? By 3? By 5? By 6? By 10?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655229161\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-272\" class=\"unnumbered unstyled\" summary=\".\" width=\"100%\">\r\n<tbody>\r\n<tr>\r\n<td>Is 5,625 divisible by 2?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Does it end in 0,2,4,6, or 8?<\/td>\r\n<td>No.\r\n5,625 is not divisible by 2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is 5,625 divisible by 3?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What is the sum of the digits?<\/td>\r\n<td>\\(5+6+2+5=18\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the sum divisible by 3?<\/td>\r\n<td>Yes. 5,625 is divisble by 3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is 5,625 divisible by 5 or 10?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What is the last digit? It is 5.<\/td>\r\n<td>5,625 is divisble by 5 but not by 10.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is 5,625 divisible by 6?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is it divisible by both 2 or 3?<\/td>\r\n<td>No, 5,625 is not divisible by 2, so 5,625 is not divisible by 6.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655196872\" data-type=\"problem\">\r\n<p id=\"fs-id1170655200166\">Determine whether 4,962 is divisible by 2, by 3, by 5, by 6, and by 10<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655200170\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655200173\">by 2, 3, and 6<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655200185\" data-type=\"problem\">\r\n<p id=\"fs-id1170655200187\">Determine whether 3,765 is divisible by 2, by 3, by 5, by 6, and by 10<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655247400\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655247402\">by 3 and 5<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Find Prime Factorization and Least Common Multiples<\/h1>\r\n<p id=\"fs-id1170655247415\">In mathematics, there are often several ways to talk about the same ideas. So far, we\u2019ve seen that if <em data-effect=\"italics\">m<\/em> is a multiple of <em data-effect=\"italics\">n<\/em>, we can say that <em data-effect=\"italics\">m<\/em> is divisible by <em data-effect=\"italics\">n<\/em>. For example, since 72 is a multiple of 8, we say 72 is divisible by 8. Since 72 is a multiple of 9, we say 72 is divisible by 9. We can express this still another way.<\/p>\r\n<p id=\"fs-id1170655224271\">Since \\(8\\cdot 9=72\\), we say that 8 and 9 are factors of 72. When we write \\(72=8\\cdot 9\\), we say we have factored 72<\/p>\r\n<span id=\"fs-id1170655160732\" data-type=\"media\" data-alt=\"An image shows the equation 8 times 9 equals 72. Written below the expression 8 times 9 is a curly bracket and the word \u201cfactors\u201d while written below 72 is a horizontal bracket and the word \u201cproduct\u201d.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_014_img_new.jpg\" alt=\"An image shows the equation 8 times 9 equals 72. Written below the expression 8 times 9 is a curly bracket and the word \u201cfactors\u201d while written below 72 is a horizontal bracket and the word \u201cproduct\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170655223714\">Other ways to factor 72 are \\(1\\cdot 72,2\\cdot 36,3\\cdot 24,4\\cdot 18,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}6\\cdot 12\\). Seventy-two has many factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, and 72<\/p>\r\n\r\n<div id=\"fs-id1170655247305\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Factors<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(a\\cdot b=m\\), then <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are factors of <em data-effect=\"italics\">m<\/em>.\r\n\r\n<\/div>\r\n<\/div>\r\nSome numbers, like 72, have many factors. Other numbers have only two factors.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655269956\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Prime Number and Composite Number<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA <strong>prime number<\/strong> is a counting number greater than 1, whose only factors are 1 and itself.\r\n\r\nA composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.\r\n\r\n<\/div>\r\n<\/div>\r\nThe counting numbers from 2 to 19 are listed in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_015_img_new\">Figure 4<\/a>, with their factors. Make sure to agree with the \u201cprime\u201d or \u201ccomposite\u201d label for each!\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"CNX_ElemAlg_Figure_01_01_015_img_new\" class=\"bc-figure figure\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"881\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_015_img_new.jpg\" alt=\"A table is shown with eleven rows and seven columns. The first row is a header row, and each cell labels the contents of the column below it. In the header row, the first three cells read from left to right \u201cNumber\u201d, \u201cFactors\u201d, and \u201cPrime or Composite?\u201d The entire fourth column is blank. The last three cells read from left to right \u201cNumber\u201d, \u201cFactor\u201d, and \u201cPrime or Composite?\u201d again. In each subsequent row, the first cell contains a number, the second contains its factors, and the third indicates whether the number is prime or composite. The three columns to the left of the blank middle column contain this information for the number 2 through 10, and the three columns to the right of the blank middle column contain this information for the number 11 through 19. On the left side of the blank column, in the first row below the header row, the cells read from left to right: \u201c2\u201d, \u201c1,2\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c3\u201d, \u201c1,3\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c4\u201d, \u201c1,2,4\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c5\u201d, \u201c1,5\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c6\u201d, \u201c1,2,3,6\u201d and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c7\u201d, \u201c1,7\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c8\u201d, \u201c1,2,4,8\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c9\u201d, \u201c1,3,9\u201d, and \u201cComposite\u201d. In the bottom row, the cells read from left to right: \u201c10\u201d, \u201c1,2,5,10\u201d, and \u201cComposite\u201d. On the right side of the blank column, in the first row below the header row, the cells read from left to right: \u201c11\u201d, \u201c1,11\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c12\u201d, \u201c1,2,3,4,6,12\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c13\u201d, \u201c1,13\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right \u201c14\u201d, \u201c1,2,7,14\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c15\u201d, \u201c1,3,5,15\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c16\u201d, \u201c1,2,4,8,16\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right, \u201c17\u201d, \u201c1,17\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right, \u201c18\u201d, \u201c1,2,3,6,9,18\u201d, and \u201cComposite\u201d. In the bottom row, the cells read from left to right: \u201c19\u201d, \u201c1,19\u201d, and \u201cPrime\u201d.\" width=\"881\" height=\"264\" data-media-type=\"image\/jpeg\" \/> Figure 4[\/caption]\r\n\r\n<\/div>\r\n<p id=\"fs-id1170655219626\">The prime number<strong data-effect=\"bold\">s<\/strong> less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Notice that the only even prime number is 2<\/p>\r\n<p id=\"fs-id1170655205294\">A composite number can be written as a unique <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of primes. This is called the prime factorization of the number. Finding the prime factorization of a composite number will be useful later in this course.<\/p>\r\n\r\n<div id=\"fs-id1170655205301\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Prime Factorization<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe prime factorization of a number is the product of prime numbers that equals the number.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655205314\">To find the prime factorization of a composite number, find any two factors of the number and use them to create two branches. If a factor is prime, that branch is complete. Circle that prime!<\/p>\r\n<p id=\"fs-id1170655206101\">If the factor is not prime, find two factors of the number and continue the process. Once all the branches have circled primes at the end, the factorization is complete. The composite number can now be written as a product of prime numbers.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">Factor 48.<\/div>\r\n<div data-type=\"title\"><\/div>\r\n<div id=\"fs-id1170655206108\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655206120\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1170655194612\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Find two factors whose product is the given number. Use these numbers to create two branches.\u201d The second cell contains the algebraic equation 48 equals 2 times 24. In the third cell, there is a factor tree with 48 at the top. Two branches descend from 48 and terminate at 2 and 24 respectively.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Find two factors whose product is the given number. Use these numbers to create two branches.\u201d The second cell contains the algebraic equation 48 equals 2 times 24. In the third cell, there is a factor tree with 48 at the top. Two branches descend from 48 and terminate at 2 and 24 respectively.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655105895\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. If a factor is prime, that branch is complete. Circle the prime.\u201d In the second cell, the instructions say: \u201c2 is prime. Circle the prime.\u201d In the third cell, the factor tree from step 1 is repeated, but the 2 at the bottom of the tree is now circled.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. If a factor is prime, that branch is complete. Circle the prime.\u201d In the second cell, the instructions say: \u201c2 is prime. Circle the prime.\u201d In the third cell, the factor tree from step 1 is repeated, but the 2 at the bottom of the tree is now circled.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654967999\" data-type=\"media\" data-alt=\"One row down, the first cell says: \u201cStep 3. If a factor is not prime, write it as the product of two factors and continue the process.\u201d In the second cell, the instructions say: \u201c24 is not prime. Break it into 2 more factors.\u201d The third cell contains the original factor tree, with 48 at the top and two downward-pointing branches terminating at 2, which is underlined, and 24. Two more branches descend from 24 and terminate at 4 and 6 respectively. One line down, the instructions in the middle of the cell say \u201c4 and 6 are not prime. Break them each into two factors.\u201d In the cell on the right, the factor tree is repeated once more. Two branches descend from the 4 and terminate at 2 and 2. Both 2s are circled. Two more branches descend from 6 and terminate at a 2 and a 3, which are both circled. The instructions on the left say \u201c2 and 3 are prime, so circle them.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016c_new.jpg\" alt=\"One row down, the first cell says: \u201cStep 3. If a factor is not prime, write it as the product of two factors and continue the process.\u201d In the second cell, the instructions say: \u201c24 is not prime. Break it into 2 more factors.\u201d The third cell contains the original factor tree, with 48 at the top and two downward-pointing branches terminating at 2, which is underlined, and 24. Two more branches descend from 24 and terminate at 4 and 6 respectively. One line down, the instructions in the middle of the cell say \u201c4 and 6 are not prime. Break them each into two factors.\u201d In the cell on the right, the factor tree is repeated once more. Two branches descend from the 4 and terminate at 2 and 2. Both 2s are circled. Two more branches descend from 6 and terminate at a 2 and a 3, which are both circled. The instructions on the left say \u201c2 and 3 are prime, so circle them.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655089548\" data-type=\"media\" data-alt=\"In the bottom row, the first cell says: \u201cStep 4. Write the composite number as the product of all the circled primes.\u201d The second cell is left blank. The third cell contains the algebraic equation 48 equals 2 times 2 times 2 times 2 times 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016d_new.jpg\" alt=\"In the bottom row, the first cell says: \u201cStep 4. Write the composite number as the product of all the circled primes.\u201d The second cell is left blank. The third cell contains the algebraic equation 48 equals 2 times 2 times 2 times 2 times 3.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170655194594\">We say \\(2\\cdot 2\\cdot 2\\cdot 2\\cdot 3\\) is the prime factorization of 48. We generally write the primes in ascending order. Be sure to multiply the factors to verify your answer!<\/p>\r\n<p id=\"fs-id1170655219541\">If we first factored 48 in a different way, for example as \\(6\\cdot 8\\), the result would still be the same. Finish the prime factorization and verify this for yourself.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655189533\" data-type=\"problem\">\r\n<p id=\"fs-id1170655189535\">Find the prime factorization of 80.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655189540\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655189542\">\\(2\\cdot 2\\cdot 2\\cdot 2\\cdot 5\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655206367\" data-type=\"problem\">\r\n<p id=\"fs-id1170655206369\">Find the prime factorization of 60.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655206373\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655206375\">\\(2\\cdot 2\\cdot 3\\cdot 5\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Find the Prime Factorization of a Composite Number.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166423940771\" class=\"stepwise\" type=\"1\">\r\n \t<li>Find two factors whose product is the given number, and use these numbers to create two branches.<\/li>\r\n \t<li>If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.<\/li>\r\n \t<li>If a factor is not prime, write it as the product of two factors and continue the process.<\/li>\r\n \t<li>Write the composite number as the product of all the circled primes.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655206361\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655206365\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655206373\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655226116\" data-type=\"problem\">\r\n<p id=\"fs-id1170655226118\">Find the prime factorization of 252<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655226122\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"fs-id1167834252648\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns with written instructions on the left and a factor tree on the right. The first line of instructions on the left say: \u201cStep 1. Find two factors whose product is 252. 12 and 21 are not prime.\u201d On the right is the top of the factor tree, which starts with 252. Two branches descend from the 252 and terminate at 12 and 21 respectively. On the left, the instructions say \u201cBreak 12 and 21 intwo two more factors. Continue until all primes are factored.\u201d On the right, two branches descend from 21 and terminate at 3 and 7, which are both prime and therefore circled. Two branches also descend from 12 and terminate at 2 and 6 respectively. 2 is prime and therefore circled. Two more branches descend from 6 and terminate at 2 and 3, which are both prime and therefore circled. On the bottom row of the figure, the instructions on the left say: \u201cStep 2. Write 252 as the product of all the circled primes.\u201d On the right is the algebraic equation 252 equals 2 times 2 times 3 times 3 times 7.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 1.<\/strong> Find two factors whose product is 252. 12 and 21 are not prime.\r\n\r\nBreak 12 and 21 into two more factors. Continue until all primes are factored.<\/td>\r\n<td><span id=\"fs-id1167835262266\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_017_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 2.<\/strong> Write 252 as the product of all the circled primes.<\/td>\r\n<td>\\(252=2\\cdot 2\\cdot 3\\cdot 3\\cdot 7\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655229695\" data-type=\"problem\">\r\n<p id=\"fs-id1170655229697\">Find the prime factorization of 126<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655229702\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655229704\">\\(2\\cdot 3\\cdot 3\\cdot 7\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655270014\" data-type=\"problem\">\r\n<p id=\"fs-id1170655270016\">Find the prime factorization of 294<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655270020\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655270022\">\\(2\\cdot 3\\cdot 7\\cdot 7\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655189637\">One of the reasons we look at multiples and primes is to use these techniques to find the least common multiple of two numbers. This will be useful when we add and subtract fractions with different <span class=\"no-emphasis\" data-type=\"term\">denominator<\/span>s. Two methods are used most often to find the least common multiple and we will look at both of them.<\/p>\r\n<p id=\"fs-id1170655189651\">The first method is the Listing Multiples Method. To find the least common multiple of 12 and 18, we list the first few multiples of 12 and 18:<\/p>\r\n<span id=\"fs-id1170655189662\" data-type=\"media\" data-alt=\"Two rows of numbers are shown. The first row begins with 12, followed by a colon, then 12, 24, 36, 48, 60, 72, 84, 96, 108, and an elipsis. 36, 72, and 108 are bolded written in red. The second row begins with 18, followed by a colon, then 18, 36, 54, 72, 90, 108, and an elipsis. Again, the numbers 36, 72, and 108 are bolded written in red. On the line below is the phrase \u201cCommon Multiples\u201d, a colon and the numbers 36, 72, and 108, written in red. One line below is the phrase \u201cLeast Common Multiple\u201d, a colon and the number 36, written in blue.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_018_img_new.jpg\" alt=\"Two rows of numbers are shown. The first row begins with 12, followed by a colon, then 12, 24, 36, 48, 60, 72, 84, 96, 108, and an elipsis. 36, 72, and 108 are bolded written in red. The second row begins with 18, followed by a colon, then 18, 36, 54, 72, 90, 108, and an elipsis. Again, the numbers 36, 72, and 108 are bolded written in red. On the line below is the phrase \u201cCommon Multiples\u201d, a colon and the numbers 36, 72, and 108, written in red. One line below is the phrase \u201cLeast Common Multiple\u201d, a colon and the number 36, written in blue.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170655189659\">Notice that some numbers appear in both lists. They are the <strong data-effect=\"bold\">common multiples<\/strong> of 12 and 18<\/p>\r\n<p id=\"fs-id1170655178513\">We see that the first few common multiples of 12 and 18 are 36, 72, and 108. Since 36 is the smallest of the common multiples, we call it the <em data-effect=\"italics\">least common multiple.<\/em> We often use the abbreviation LCM.<\/p>\r\n\r\n<div id=\"fs-id1170655178531\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Least Common Multiple<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655178544\">The procedure box lists the steps to take to find the LCM using the prime factors method we used above for 12 and 18<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Find the Least Common Multiple by Listing Multiples.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\"><\/div>\r\n<ol id=\"fs-id1166426329693\" class=\"stepwise\" type=\"1\">\r\n \t<li>List several multiples of each number.<\/li>\r\n \t<li>Look for the smallest number that appears on both lists.<\/li>\r\n \t<li>This number is the LCM.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655178548\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655189105\" data-type=\"problem\">\r\n<p id=\"fs-id1170655189107\">Find the least common multiple of 15 and 20 by listing multiples.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655189111\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"fs-id1167831872566\" class=\"unnumbered unstyled can-break\" summary=\"This figure is divided into two coulmns. In the upper left, the instructions say: \u201cMake lists of the first few multiples of 15 and of 20, and use them to find the least common multiple.\u201d The upper right section has two rows of numbers. The first begins with 15 followed by a colon, then 15, 30, 45, 60, 75, 90, 105, and 120. 60 is bolded and written in red. The second row begins with 20 followed by a colon, then 20, 40, 60, 80, 100, 120, 140, and 160. 60 is again bolded and written in red. The lower left section reads \u201cLook for the smallest number that appears in both lists.\u201d The lower right section reads \u201cThe first number to appear on both lists is 60, so 60 is the least common multiple of 15 and 20.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Make lists of the first few multiples of 15 and of 20, and use them to find the least common multiple.<\/td>\r\n<td><span id=\"fs-id1167832051958\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_019_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for the smallest number that appears in both lists.<\/td>\r\n<td>The first number to appear on both lists is 60, so 60 is the least common multiple of 15 and 20.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655206417\">Notice that 120 is in both lists, too. It is a common multiple, but it is not the <em data-effect=\"italics\">least<\/em> common multiple.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655206435\" data-type=\"problem\">\r\n<p id=\"fs-id1170655206437\">Find the least common multiple by listing multiples: 9 and 12<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655206442\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655206444\">36<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655206456\" data-type=\"problem\">\r\n<p id=\"fs-id1170655206459\">Find the least common multiple by listing multiples: 18 and 24<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655206463\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655206465\">72<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nOur second method to find the least common multiple of two numbers is to use The Prime Factors Method. Let\u2019s find the LCM of 12 and 18 again, this time using their prime factors.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">Find the Least Common Multiple (LCM) of 12 and 18 using the prime factors method.<\/div>\r\n<div id=\"fs-id1170655199673\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655199684\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1170655199720\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Write each number as a product of primes.\u201d The second cell is left blank. In the third cell, there are two factor trees. In the first factor tree, two branches descend from 18 and terminate at 3 and 6 respectively. The 3 is prime and therefore circled. Two more branches descend from the 6 and terminate in 2 and 3, both of which are circled. In the second factor tree, two branches descend from 12 and terminate at 3 and 4. The 3 is circled. Two more branches descend from 4, terminating at 2 and 2, both of which are circled.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Write each number as a product of primes.\u201d The second cell is left blank. In the third cell, there are two factor trees. In the first factor tree, two branches descend from 18 and terminate at 3 and 6 respectively. The 3 is prime and therefore circled. Two more branches descend from the 6 and terminate in 2 and 3, both of which are circled. In the second factor tree, two branches descend from 12 and terminate at 3 and 4. The 3 is circled. Two more branches descend from 4, terminating at 2 and 2, both of which are circled.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654905180\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. List the primes of each number. Match primes vertically when possible.\u201d In the second cell, the instructions say: \u201cList the primes of 12. List the primes of 18. Line up with the primes of 12 when possible. If not create a new column.\u201d The third cell contains the prime factorization of 12 written as the equation 12 equals 2 times 2 times 3. Below this equation is another showing the prime factorization of 18 written as the equation 18 equals 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 in the prime factorization of 12 aligns with the 2 in the prime factorization of 18. Under the second 2 in the prime factorization of 12 is a gap in the prime factorization of 18. Under the 3 in the prime factorization of 12 is the first 3 in the prime factorization of 18. The second 3 in the prime factorization has no factors above it from the prime factorization of 12.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. List the primes of each number. Match primes vertically when possible.\u201d In the second cell, the instructions say: \u201cList the primes of 12. List the primes of 18. Line up with the primes of 12 when possible. If not create a new column.\u201d The third cell contains the prime factorization of 12 written as the equation 12 equals 2 times 2 times 3. Below this equation is another showing the prime factorization of 18 written as the equation 18 equals 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 in the prime factorization of 12 aligns with the 2 in the prime factorization of 18. Under the second 2 in the prime factorization of 12 is a gap in the prime factorization of 18. Under the 3 in the prime factorization of 12 is the first 3 in the prime factorization of 18. The second 3 in the prime factorization has no factors above it from the prime factorization of 12.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655083625\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cBring down the number from each column.\u201d The second cell is blank. The third cell contains the prime factorizations of 12 and 18 again, illustrated as two equations aligned just as they were before. This time, a horizontal line is drawn under the prime factorization of 18. Below this line is the equation LCM equal to 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 12 through the prime factorization of 18 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 12 and continues down through the 2 in the prime factorization of 18, ending with the first 2 in the LCM. The second arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The third arrow starts at the 3 in the prime factorization of 12 and continues down through the first 3 in the prime factorization of 18, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 18 and points down to the second 3 in the LCM.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020c_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cBring down the number from each column.\u201d The second cell is blank. The third cell contains the prime factorizations of 12 and 18 again, illustrated as two equations aligned just as they were before. This time, a horizontal line is drawn under the prime factorization of 18. Below this line is the equation LCM equal to 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 12 through the prime factorization of 18 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 12 and continues down through the 2 in the prime factorization of 18, ending with the first 2 in the LCM. The second arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The third arrow starts at the 3 in the prime factorization of 12 and continues down through the first 3 in the prime factorization of 18, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 18 and points down to the second 3 in the LCM.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654935281\" data-type=\"media\" data-alt=\"In the bottom row of the table, the first cell says: \u201cStep 4: Multiply the factors.\u201d The second cell is bank. The third cell contains the equation LCM equals 36.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020d_new.jpg\" alt=\"In the bottom row of the table, the first cell says: \u201cStep 4: Multiply the factors.\u201d The second cell is bank. The third cell contains the equation LCM equals 36.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655199709\">Notice that the prime factors of 12 \\(\\left(2\\cdot 2\\cdot 3\\right)\\) and the prime factors of 18 \\(\\left(2\\cdot 3\\cdot 3\\right)\\) are included in the LCM \\(\\left(2\\cdot 2\\cdot 3\\cdot 3\\right)\\). So 36 is the least common multiple of 12 and 18<\/p>\r\n<p id=\"fs-id1170655195905\">By matching up the common primes, each common prime factor is used only once. This way you are sure that 36 is the <em data-effect=\"italics\">least<\/em> common multiple.<\/p>\r\n\r\n<div id=\"fs-id1170655195914\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655195919\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655195921\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655195921\" data-type=\"problem\">\r\n<p id=\"fs-id1170655195923\">Find the LCM using the prime factors method: 9 and 12<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655195927\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655195929\">36<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655195942\" data-type=\"problem\">\r\n<p id=\"fs-id1170655195944\">Find the LCM using the prime factors method: 18 and 24<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655195948\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655195950\">72<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Find the Least Common Multiple Using the Prime Factors Method.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166426408882\" class=\"stepwise\" type=\"1\">\r\n \t<li>Write each number as a product of primes.<\/li>\r\n \t<li>List the primes of each number. Match primes vertically when possible.<\/li>\r\n \t<li>Bring down the columns.<\/li>\r\n \t<li>Multiply the factors.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655229842\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655229887\" data-type=\"problem\">\r\n<p id=\"fs-id1170655229889\">Find the Least Common Multiple (LCM) of 24 and 36 using the prime factors method.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655229893\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"fs-id1167826967413\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. The first three lines of instructions on the left say \u201cFind the primes of 24 and 36. Match primes vertically when possible. Bring down all columns.\u201d On the right, the prime factorization of 24 is written as the equation 24 equals 2 times 2 times 2 times 3. Below this equation is another showing the prime factorization of 36 written as the equation 36 equals 2 times 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 and the second 2 in the prime factorization of 24 aligns with the first 2 and the second 2 in the prime factorization of 36. Under the third 2 in the prime factorization of 24 is a gap in the prime factorization of 36. Under the 3 in the prime factorization of 24 is the first 3 in the prime factorization of 36. The second 3 in the prime factorization of 36 has no factors above it from the prime factorization of 24. A horizontal line is drawn under the prime factorization of 36. Below this line is the equation LCM equal to 2 times 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 24 through the prime factorization of 36 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 24 and continues down through the 2 in the prime factorization of 36, ending with the first 2 in the LCM. The second arrow starts at the second 2 in the prime factorization of 24 and continues down through the second 2 in the prime factorization of 36, ending with the second 2 in the LCM. The third arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The fourth arrow starts at the 3 in the prime factorization of 24 and continues down through the first 3 in the prime factorization of 36, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 36 and points down to the second 3 in the LCM. One row down, the instructions on the left say \u201cMultiply the factors.\u201d On the right is the equation LCM equals 72. One line down, on the right, is the text \u201cThe LCM of 24 and 36 is 72.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Find the prime factors of 24 and 36.\r\nMatch primes vertically when possible. Bring down all columns.<\/td>\r\n<td><span id=\"fs-id1167835321942\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the factors.<\/td>\r\n<td><span id=\"fs-id1167832116015\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>The LCM of 24 and 36 is 72.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655222007\" data-type=\"problem\">\r\n<p id=\"fs-id1170655222009\">Find the LCM using the prime factors method: 21 and 28<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655222013\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655222015\">84<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655222028\" data-type=\"problem\">\r\n<p id=\"fs-id1170655222030\">Find the LCM using the prime factors method: 24 and 32<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655222054\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170655222056\">96<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1170655178412\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Place Value<\/strong> as in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_002_new\">Figure 2<\/a>.<\/li>\r\n \t<li><strong data-effect=\"bold\">Name a Whole Number in Words<\/strong>\r\n<ol id=\"fs-id1166426408194\" class=\"stepwise\" type=\"1\">\r\n \t<li>Start at the left and name the number in each period, followed by the period name.<\/li>\r\n \t<li>Put commas in the number to separate the periods.<\/li>\r\n \t<li>Do not name the ones period.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Write a Whole Number Using Digits<\/strong>\r\n<ol id=\"fs-id1166426408220\" class=\"stepwise\" type=\"1\">\r\n \t<li>Identify the words that indicate periods. (Remember the ones period is never named.)<\/li>\r\n \t<li>Draw 3 blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\r\n \t<li>Name the number in each period and place the digits in the correct place value position.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Round Whole Numbers<\/strong>\r\n<ol id=\"fs-id1166419319557\" class=\"stepwise\" type=\"1\">\r\n \t<li>Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.<\/li>\r\n \t<li>Underline the digit to the right of the given place value.<\/li>\r\n \t<li>Is this digit greater than or equal to 5?\r\n<ul id=\"fs-id1166419319583\" data-bullet-style=\"bullet\">\r\n \t<li>Yes\u2014add 1 to the digit in the given place value.<\/li>\r\n \t<li>No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Replace all digits to the right of the given place value with zeros.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Divisibility Tests:<\/strong> A number is divisible by:\r\n<ul id=\"fs-id1170655206214\" data-bullet-style=\"open-circle\">\r\n \t<li>2 if the last digit is 0, 2, 4, 6, or 8.<\/li>\r\n \t<li>3 if the sum of the digits is divisible by 3.<\/li>\r\n \t<li>5 if the last digit is 5 or 0.<\/li>\r\n \t<li>6 if it is divisible by both 2 and 3.<\/li>\r\n \t<li>10 if it ends with 0.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Find the Prime Factorization of a Composite Number<\/strong>\r\n<ol id=\"fs-id1166423744411\" class=\"stepwise\" type=\"1\">\r\n \t<li>Find two factors whose product is the given number, and use these numbers to create two branches.<\/li>\r\n \t<li>If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.<\/li>\r\n \t<li>If a factor is not prime, write it as the product of two factors and continue the process.<\/li>\r\n \t<li>Write the composite number as the product of all the circled primes.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Find the Least Common Multiple by Listing Multiples<\/strong>\r\n<ol id=\"fs-id1166421706928\" class=\"stepwise\" type=\"1\">\r\n \t<li>List several multiples of each number.<\/li>\r\n \t<li>Look for the smallest number that appears on both lists.<\/li>\r\n \t<li>This number is the LCM.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Find the Least Common Multiple Using the Prime Factors Method<\/strong>\r\n<ol id=\"fs-id1166421706953\" class=\"stepwise\" type=\"1\">\r\n \t<li>Write each number as a product of primes.<\/li>\r\n \t<li>List the primes of each number. Match primes vertically when possible.<\/li>\r\n \t<li>Bring down the columns.<\/li>\r\n \t<li>Multiply the factors.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<dl id=\"fs-id1166424132611\">\r\n \t<dd id=\"fs-id1166424132616\">\r\n<div class=\"textbox shaded\">\r\n<dl id=\"fs-id1166426314283\">\r\n \t<dt>composite number<\/dt>\r\n \t<dd id=\"fs-id1166426314289\">A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632702\">\r\n \t<dt>counting numbers<\/dt>\r\n \t<dd id=\"fs-id1166421632707\">The counting numbers are the numbers 1, 2, 3, \u2026<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632717\">\r\n \t<dt>divisible by a number<\/dt>\r\n \t<dd id=\"fs-id1166421632723\">If a number \\(m\\) is a multiple of \\(n\\), then \\(m\\) is divisible by \\(n\\). (If 6 is a multiple of 3, then 6 is divisible by 3.)<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632750\">\r\n \t<dt>factors<\/dt>\r\n \t<dd id=\"fs-id1166421632755\">If \\(a\u00b7b=m\\), then \\(a\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b\\) are factors of \\(m\\). Since 3 \u00b7 4 = 12, then 3 and 4 are factors of 12.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632812\">\r\n \t<dt>least common multiple<\/dt>\r\n \t<dd id=\"fs-id1166421632818\">The least common multiple of two numbers is the smallest number that is a multiple of both numbers.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632827\">\r\n \t<dt>multiple of a number<\/dt>\r\n \t<dd id=\"fs-id1166421632833\">A number is a multiple of <em data-effect=\"italics\">n<\/em> if it is the product of a counting number and <em data-effect=\"italics\">n<\/em>.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632848\">\r\n \t<dt>number line<\/dt>\r\n \t<dd id=\"fs-id1166421632853\">A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166421632864\">\r\n \t<dt>origin<\/dt>\r\n \t<dd id=\"fs-id1166421632869\">The origin is the point labeled 0 on a number line.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166424132582\">\r\n \t<dt>prime factorization<\/dt>\r\n \t<dd id=\"fs-id1166424132587\">The prime factorization of a number is the product of prime numbers that equals the number.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166424132596\">\r\n \t<dt>prime number<\/dt>\r\n \t<dd id=\"fs-id1166424132602\">A prime number is a counting number greater than 1, whose only factors are 1 and itself.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166424132611\">\r\n \t<dt>whole numbers<\/dt>\r\n \t<dd id=\"fs-id1166424132616\">The whole numbers are the numbers 0, 1, 2, 3, ....<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<h2>Use Place Value with Whole Numbers<\/h2>\r\n<p id=\"fs-id1166421707006\">In the following exercises, find the place value of each digit in the given numbers.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">1. 51,493\r\na) 1\r\nb) 4\r\nc) 9\r\nd) 5\r\ne) 3<\/td>\r\n<td style=\"width: 50%\">2. 87,210\r\na) 2\r\nb) 8\r\nc) 0\r\nd) 7\r\ne) 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">3. 164,285\r\na) 5\r\nb) 6\r\nc) 1\r\nd) 8\r\ne) 2<\/td>\r\n<td style=\"width: 50%\">4. 395,076\r\na) 5\r\nb) 3\r\nc) 7\r\nd) 0\r\ne) 9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">5. 93,285,170\r\na) 9\r\nb) 8\r\nc) 7\r\nd) 5\r\ne) 3<\/td>\r\n<td style=\"width: 50%\">6. 36,084,215\r\na) 8\r\nb) 6\r\nc) 5\r\nd) 4\r\ne) 3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">7. 7,284,915,860,132\r\na) 7\r\nb) 4\r\nc) 5\r\nd) 3\r\ne) 0<\/td>\r\n<td style=\"width: 50%\">8. 2,850,361,159,433\r\na) 9\r\nb) 8\r\nc) 6\r\nd) 4\r\ne) 2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655227536\">In the following exercises, name each number using words.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 90px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">9. 1,078<\/td>\r\n<td style=\"width: 50%;height: 15px\">10. 5,902<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">11. 364,510<\/td>\r\n<td style=\"width: 50%;height: 15px\">12. 146,023<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">13. 5,846,103<\/td>\r\n<td style=\"width: 50%;height: 15px\">14. 1,458,398<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">15. 37,889,005<\/td>\r\n<td style=\"width: 50%;height: 15px\">16. 62,008,465<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655206924\">In the following exercises, write each number as a whole number using digits.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 75px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">17. four hundred twelve<\/td>\r\n<td style=\"width: 50%;height: 15px\">18. two hundred fifty-three<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">19. thirty-five thousand, nine hundred seventy-five<\/td>\r\n<td style=\"width: 50%;height: 15px\">20. sixty-one thousand, four hundred fifteen<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">21. eleven million, forty-four thousand, one hundred sixty-seven<\/td>\r\n<td style=\"width: 50%;height: 15px\">22. eighteen million, one hundred two thousand, seven hundred eighty-three<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">23. three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen<\/td>\r\n<td style=\"width: 50%;height: 15px\">24. eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655194762\">In the following, round to the indicated place value.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194769\">25. Round to the nearest ten.<\/p>\r\n<p id=\"fs-id1170655194772\">a) 386 b) 2,931<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194788\">26. Round to the nearest ten.<\/p>\r\n<p id=\"fs-id1170655194792\">a) 792 b) 5,647<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194808\">27. Round to the nearest hundred.<\/p>\r\n<p id=\"fs-id1170655194811\">a) 13,748 b) 391,794<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194827\">28. Round to the nearest hundred.<\/p>\r\n<p id=\"fs-id1170655194830\">a) 28,166 b) 481,628<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194846\">29. Round to the nearest ten.<\/p>\r\n<p id=\"fs-id1170655194849\">a) 1,492 b) 1,497<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194865\">30. Round to the nearest ten.<\/p>\r\n<p id=\"fs-id1170655194869\">a) 2,791 b) 2,795<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194886\">31. Round to the nearest hundred.<\/p>\r\n<p id=\"fs-id1170655194889\">a) 63,994 b) 63,940<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170655194906\">32. Round to the nearest hundred.<\/p>\r\n<p id=\"fs-id1170655194910\">a) 49,584 b) 49,548<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655198323\">In the following exercises, round each number to the nearest a) hundred, b) thousand, c) ten thousand.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">33. 392,546<\/td>\r\n<td style=\"width: 50%\">34. 619,348<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">35. 2,586,991<\/td>\r\n<td style=\"width: 50%\">36. 4,287,965<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Identify Multiples and Factors<\/h2>\r\n<p id=\"fs-id1170655198399\">In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 120px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">37. 84<\/td>\r\n<td style=\"width: 50%;height: 15px\">38. 9,696<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">39. 75<\/td>\r\n<td style=\"width: 50%;height: 15px\">40. 78<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">41. 900<\/td>\r\n<td style=\"width: 50%;height: 15px\">42. 800<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">43. 986<\/td>\r\n<td style=\"width: 50%;height: 15px\">44. 942<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">45. 350<\/td>\r\n<td style=\"width: 50%;height: 15px\">46. 550<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">47. 22,335<\/td>\r\n<td style=\"width: 50%;height: 15px\">48. 39,075<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Find Prime Factorizations and Least Common Multiples<\/h2>\r\n<p id=\"fs-id1170655196091\">In the following exercises, find the prime factorization.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 121px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">49. 86<\/td>\r\n<td style=\"width: 50%;height: 16px\">50. 78<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">51. 132<\/td>\r\n<td style=\"width: 50%;height: 15px\">52. 455<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">53. 693<\/td>\r\n<td style=\"width: 50%;height: 15px\">54. 400<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">55. 432<\/td>\r\n<td style=\"width: 50%;height: 15px\">56. 627<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">57. 2,160<\/td>\r\n<td style=\"width: 50%;height: 15px\">58. 2,520<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655165795\">In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">59. 8, 12<\/td>\r\n<td style=\"width: 50%\">60. 4, 3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">61. 12, 16<\/td>\r\n<td style=\"width: 50%\">62. 30, 40<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">63. 20, 30<\/td>\r\n<td style=\"width: 50%\">64. 44, 55<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655170829\">In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">65. 8, 12<\/td>\r\n<td style=\"width: 50%\">66. 12, 16<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">67. 28, 40<\/td>\r\n<td style=\"width: 50%\">68. 84, 90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">69. 55, 88<\/td>\r\n<td style=\"width: 50%\">70. 60, 72<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Everyday Math<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 106px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">71. <strong data-effect=\"bold\">Writing a Check<\/strong> Jorge bought a car for \\$24,493. He paid for the car with a check. Write the purchase price in words.<\/td>\r\n<td style=\"width: 50%;height: 16px\">72. <strong data-effect=\"bold\">Writing a Check<\/strong> Marissa\u2019s kitchen remodeling cost \\$18,549. She wrote a check to the contractor. Write the amount paid in words.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">73. <strong data-effect=\"bold\">Buying a Car<\/strong> Jorge bought a car for \\$24,493. Round the price to the nearest a) ten b) hundred c) thousand; and d) ten-thousand.<\/td>\r\n<td style=\"width: 50%;height: 15px\">74. <strong data-effect=\"bold\">Remodeling a Kitchen<\/strong> Marissa\u2019s kitchen remodeling cost \\$18,549, Round the cost to the nearest a) ten b) hundred c) thousand and d) ten-thousand.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">75. <strong data-effect=\"bold\">Population<\/strong> The population of China was 1,339,724,852 on November 1, 2010. Round the population to the nearest a) billion b) hundred-million; and c) million.<\/td>\r\n<td style=\"width: 50%;height: 15px\">76. <strong data-effect=\"bold\">Astronomy<\/strong> The average distance between Earth and the sun is 149,597,888 kilometres. Round the distance to the nearest a) hundred-million b) ten-million; and c) million.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">77. <strong data-effect=\"bold\">Grocery Shopping<\/strong> Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?<\/td>\r\n<td style=\"width: 50%;height: 15px\">78. <strong data-effect=\"bold\">Grocery Shopping<\/strong> Paper plates are sold in packages of 12 and party cups come in packs of eight. What is the smallest number that makes the plates and cups come out even?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Writing Exercises<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">79. What is the difference between prime numbers and composite numbers?<\/td>\r\n<td style=\"width: 50%\">80. Give an everyday example where it helps to round numbers.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">81. Explain in your own words how to find the prime factorization of a composite number, using any method you prefer.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/dd>\r\n<\/dl>\r\n<h1>Answers<\/h1>\r\n<div data-type=\"glossary\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 310px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 35px\">\r\n<td style=\"width: 33.3333%;height: 35px\">1. a) thousands b) hundreds c) tens d) ten thousands e) ones<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">3. a) ones b) ten thousands c) hundred thousands d) tens e) hundreds<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">5. a) ten millions b) ten thousands c) tens d) thousands e) millions<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px\">\r\n<td style=\"width: 33.3333%;height: 35px\">7. a) trillions b) billions c) millions d) tens e) thousands<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">9. one thousand, seventy-eight<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">11. three hundred sixty-four thousand, five hundred ten<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px\">\r\n<td style=\"width: 33.3333%;height: 35px\">13. five million, eight hundred forty-six thousand, one hundred three<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">15. thirty-seven million, eight hundred eighty-nine thousand, five<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">17. 412<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">19. 35,975<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">21. 11,044,167<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">23. 3,226,512,017<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">25. a) 390 b) 2,930<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">27. a) 13,700 b) 391,800<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">29. a) 1,490 b) 1,500<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">31. a) 64,000 b) 63,900<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">33. a) 392,500 b) 393,000 c) 390,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">35. a) 2,587,000 b) 2,587,000 c) 2,590,000<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">37. divisible by 2, 3, and 6<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">39. divisible by 3 and 5<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">41. divisible by 2, 3, 5, 6, and 10<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">43. divisible by 2<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">45. divisible by 2, 5, and 10<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">47. divisible by 3 and 5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">49. \\(2\\cdot 43\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">51. \\(2\\cdot 2\\cdot 3\\cdot 11\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">53. \\(3\\cdot 3\\cdot 7\\cdot 11\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">55. \\(2\\cdot 2\\cdot 2\\cdot 2\\cdot 3\\cdot 3\\cdot 3\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">57. \\(2\\cdot 2\\cdot 2\\cdot 2\\cdot 3\\cdot 3\\cdot 3\\cdot 5\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">59. 24<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">61. 48<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">63. 60<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">65. 24<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px\">\r\n<td style=\"width: 33.3333%;height: 35px\">67. 280<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">69. 440<\/td>\r\n<td style=\"width: 33.3333%;height: 35px\">71. twenty-four thousand, four hundred ninety-three dollars<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">73. a) \\$24,490 b) \\$24,500 c) \\$24,000 d) \\$20,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">75. a) 1,000,000,000 b) 1,300,000,000 c) 1,340,000,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">77. 40<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">79. Answers may vary.<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">81. Answers may vary.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cIntroduction to Whole Numbers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\r\n\r\n<\/div>\r\n<!-- pb_fixme -->","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use place value with whole numbers<\/li>\n<li>Identify multiples and apply divisibility tests<\/li>\n<li>Find prime factorization and least common multiples<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655154091\">As we begin our study of intermediate algebra, we need to refresh some of our skills and vocabulary. This chapter and the next will focus on whole numbers, integers, fractions, decimals, and real numbers. We will also begin our use of algebraic notation and vocabulary.<\/p>\n<h1>Use Place Value with Whole Numbers<\/h1>\n<p id=\"fs-id1170655162029\">The most basic numbers used in algebra are the numbers we use to count objects in our world: 1, 2, 3, 4, and so on. These are called the counting number<strong data-effect=\"bold\">s<\/strong>. Counting numbers are also called <em data-effect=\"italics\">natural numbers<\/em>. If we add zero to the counting numbers, we get the set of whole number<strong data-effect=\"bold\">s<\/strong>.<\/p>\n<p id=\"fs-id1170655024948\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bd39041b5d85f208f6cbfa61f4d6691e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>Counting Numbers: 1, 2, 3, \u2026<\/p>\n<p id=\"fs-id1170655082425\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bd39041b5d85f208f6cbfa61f4d6691e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>Whole Numbers: 0, 1, 2, 3, \u2026<\/p>\n<p id=\"fs-id1170655192198\">The notation \u201c\u2026\u201d is called ellipsis and means \u201cand so on,\u201d or that the pattern continues endlessly.<\/p>\n<p id=\"fs-id1170655197123\">We can visualize counting numbers and whole numbers on a number line .See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_001_new\">Figure 1<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_01_001_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left. While this number line shows only the whole numbers 0 through 6, the numbers keep going without end.<\/div>\n<figure style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/05\/CNX_ElemAlg_Figure_01_01_001_new.jpg\" alt=\"A horizontal number line with arrows on each end and values of zero to six runs along the bottom of the diagram. A second horizontal line with a left-facing arrow lies above the first and extend from zero to three. This line is labled \u201csmaller\u201d. A third horizontal line with a right-facing arrow lies above the first two, but runs from three to six and is labeled \u201clarger\u201d.\" width=\"750\" height=\"117\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 1<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1170655190408\">Our <span class=\"no-emphasis\" data-type=\"term\">number system<\/span> is called a place value system, because the value of a digit depends on its position in a number. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_002_new\">Figure 2<\/a> shows the <span class=\"no-emphasis\" data-type=\"term\">place values<\/span>. The place values are separated into groups of three, which are called periods. The periods are <em data-effect=\"italics\">ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.<\/p>\n<p>The number 5,278,194 is shown in the chart. The digit 5 is in the millions place. The digit 2 is in the hundred-thousands place. The digit 7 is in the ten-thousands place. The digit 8 is in the thousands place. The digit 1 is in the hundreds place. The digit 9 is in the tens place. The digit 4 is in the ones place.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_01_002_new\" class=\"bc-figure figure\">\n<div><\/div>\n<figure style=\"width: 377px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_002_new.jpg\" alt=\"This figure is a table illustrating the number 5,278,194 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 5, 2, 7, 8, 1, 9, 4. This means there are 5 millions, 2 hundred thousands, 7 ten thousands, 8 thousands, 1 hundreds, 9 tens, and 4 ones in the number five million two hundred seventy-nine thousand one hundred ninety-four.\" width=\"377\" height=\"289\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 2<\/figcaption><\/figure>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654978132\" data-type=\"problem\">\n<p id=\"fs-id1170655192807\">In the number 63,407,218, find the place value of each digit:<\/p>\n<ol id=\"fs-id1166421427575\" class=\"circled\" type=\"a\">\n<li>7<\/li>\n<li>0<\/li>\n<li>1<\/li>\n<li>6<\/li>\n<li>3<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1170655022351\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654968077\">Place the number in the place value chart:<\/p>\n<p><span id=\"fs-id1170655112880\" data-type=\"media\" data-alt=\"This figure is a table illustrating the number 63,407,218 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cTen millions\u201d, \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 6, 3, 4, 0, 7, 2, 1, 8. This means there are 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, and 8 ones in the number sixty-three million, four hundred seven thousand, two hundred eighteen.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_003_img_new.jpg\" alt=\"This figure is a table illustrating the number 63,407,218 within the place value system. The table is shown with a header row, labeled \u201cPlace Value\u201d, divided into a second header row labeled \u201cTrillions\u201d, \u201cBillions\u201d, \u201cMillions\u201d, \u201cThousands\u201d and \u201cOnes\u201d. Under the header \u201cTrillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred trillions\u201d, \u201cTen trillions\u201d and \u201cTrillions\u201d. Under the header \u201cBillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred billions\u201d, \u201cTen billions\u201d and \u201cBillions\u201d. Under the header \u201cMillions\u201d are three labeled columns, written from bottom to top, that read \u201cHundred millions\u201d, \u201cTen millions\u201d and \u201cMillions\u201d. Under the header \u201cThousands\u201d are three labeled columns, written from bottom to top, that read \u201cHundred thousands\u201d, \u201cTen thousands\u201d and \u201cThousands\u201d. Under the header \u201cOnes\u201d are three labeled columns, written from bottom to top, that read \u201cHundreds\u201d, \u201cTens\u201d and \u201cOnes\u201d. From left to right, below the columns labeled \u201cTen millions\u201d, \u201cMillions\u201d, \u201cHundred thousands\u201d, \u201cTen thousands\u201d, \u201cThousands\u201d, \u201cHundreds\u201d, \u201cTens\u201d, and \u201cOnes\u201d, are the following values: 6, 3, 4, 0, 7, 2, 1, 8. This means there are 6 ten millions, 3 millions, 4 hundred thousands, 0 ten thousands, 7 thousands, 2 hundreds, 1 ten, and 8 ones in the number sixty-three million, four hundred seven thousand, two hundred eighteen.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1166426398759\">a) The 7 is in the thousands place.<br \/>\nb) The 0 is in the ten thousands place.<br \/>\nc) The 1 is in the tens place.<br \/>\nd) The 6 is in the ten-millions place.<br \/>\ne) The 3 is in the millions place.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655125783\" data-type=\"problem\">\n<p id=\"fs-id1170655133227\">For the number 27,493,615, find the place value of each digit:<\/p>\n<p id=\"fs-id1170655154330\">a) 2\u2003b) 1\u2003c) 4\u2003d) 7\u2003e) 5<\/p>\n<\/div>\n<div id=\"fs-id1170655192955\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654924451\">a) ten millions b) tens c) hundred thousands d) millions e) ones<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655171837\" data-type=\"problem\">\n<p id=\"fs-id1170655171777\">For the number 519,711,641,328, find the place value of each digit:<\/p>\n<p id=\"fs-id1170655114062\">a) 9\u2003b) 4\u2003c) 2\u2003d) 6\u2003e) 7<\/p>\n<\/div>\n<div id=\"fs-id1170655129771\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655163552\">a) billions b) ten thousands c) tens d) hundred thousands e) hundred millions<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655113270\">When you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period, followed by the name of the period, without the <em data-effect=\"italics\">s<\/em> at the end. Start at the left, where the periods have the largest value. The ones period is not named. The commas separate the periods, so wherever there is a comma in the number, put a comma between the words (see <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_004_new\">Figure 3)<\/a>. The number 74,218,369 is written as seventy-four million, two hundred eighteen thousand, three hundred sixty-nine.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_01_004_new\" class=\"bc-figure figure\">\n<figure style=\"width: 503px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_004_new.jpg\" alt=\"In this figure, the numbers 74, 218 and 369 are listed in a row, separated by commas. Each number has a curly bracket beneath it with the word \u201cmillions\u201d written below the number 74, \u201cthousands\u201d written below the number 218, and \u201cones\u201d written below the number 369. A left-facing arrow points at these three words, labeling them \u201cperiods\u201d. One row down is the number \u201c74\u201d, a right-facing arrow and the words \u201cSeventy-four million\u201d followed by a comma. The next row below is the number \u201c218\u201d, a right-facing arrow and the words \u201ctwo hundred eighteen thousand\u201d followed by a comma. On the bottom row is the number \u201c369\u201d, a right-facing arrow and the words \u201cthree hundred sixty-nine\u201d.\" width=\"503\" height=\"137\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 3<\/figcaption><\/figure>\n<\/div>\n<div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Name a Whole Number in Words.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426255157\" class=\"stepwise\" type=\"1\">\n<li>Start at the left and name the number in each period, followed by the period name.<\/li>\n<li>Put commas in the number to separate the periods.<\/li>\n<li>Do not name the ones period.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655127621\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655175454\" data-type=\"problem\">\n<p id=\"fs-id1170654981580\">Name the number 8,165,432,098,710 using words.<\/p>\n<\/div>\n<div id=\"fs-id1170654857936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655134588\">Name the number in each period, followed by the period name.<\/p>\n<p><span id=\"fs-id1170655155229\" data-type=\"media\" data-alt=\"In this figure, the numbers 8, 165, 432, 098 and 710 are listed in a row, separated by commas. Each number has a horizontal bracket beneath with the word \u201ctrillions\u201d written below the number 8, \u201cbillions\u201d written below the number 165, \u201cmillions\u201d written below the number 432, \u201cthousands\u201d written below the number 098, and \u201cones\u201d written below the number 710. One row down is the number 8, a right-facing arrow and the words \u201cEight trillion\u201d followed by a comma. On the next row below is the number 165, a right-facing arrow and the words \u201cOne hundred sixty-five billion\u201d followed by a comma. On the next row below is the number 432, a right-facing arrow and the words \u201cFour hundred thirty-two million\u201d followed by a comma. On the next row below is the number \u201c098\u201d, a right-facing arrow and the words \u201cNinety-eight thousand\u201d followed by a comma. On the bottom row is the number 710, a right-facing arrow and the words \u201cSeven hundred ten\u201d.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_005_img_new.jpg\" alt=\"In this figure, the numbers 8, 165, 432, 098 and 710 are listed in a row, separated by commas. Each number has a horizontal bracket beneath with the word \u201ctrillions\u201d written below the number 8, \u201cbillions\u201d written below the number 165, \u201cmillions\u201d written below the number 432, \u201cthousands\u201d written below the number 098, and \u201cones\u201d written below the number 710. One row down is the number 8, a right-facing arrow and the words \u201cEight trillion\u201d followed by a comma. On the next row below is the number 165, a right-facing arrow and the words \u201cOne hundred sixty-five billion\u201d followed by a comma. On the next row below is the number 432, a right-facing arrow and the words \u201cFour hundred thirty-two million\u201d followed by a comma. On the next row below is the number \u201c098\u201d, a right-facing arrow and the words \u201cNinety-eight thousand\u201d followed by a comma. On the bottom row is the number 710, a right-facing arrow and the words \u201cSeven hundred ten\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654915073\">Put the commas in to separate the periods.<\/p>\n<p id=\"fs-id1170655164902\">So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4809f6fe9d730b793525b9387e302142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#44;&#49;&#54;&#53;&#44;&#52;&#51;&#50;&#44;&#48;&#57;&#56;&#44;&#55;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -4px;\" \/> is named as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655195315\" data-type=\"problem\">\n<p id=\"fs-id1170654905813\">Name the number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ed0e279aa4cfc5a215d4362accaa973f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#44;&#50;&#53;&#56;&#44;&#49;&#51;&#55;&#44;&#57;&#48;&#52;&#44;&#48;&#54;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"146\" style=\"vertical-align: -4px;\" \/> using words.<\/p>\n<\/div>\n<div id=\"fs-id1170655096352\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654989620\">nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655157875\" data-type=\"problem\">\n<p id=\"fs-id1170655162513\">Name the number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b1ec4cf65888a4219184d6d455b08e9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#44;&#56;&#54;&#52;&#44;&#51;&#50;&#53;&#44;&#54;&#49;&#57;&#44;&#48;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -4px;\" \/> using words.<\/p>\n<\/div>\n<div id=\"fs-id1170654977617\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654957397\">seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand, four<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655190403\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655075933\" data-type=\"exercise\">\n<div id=\"fs-id1170655195315\" data-type=\"problem\">We are now going to reverse the process by writing the digits from the name of the number. To write the number in digits, we first look for the clue words that indicate the periods. It is helpful to draw three blanks for the needed periods and then fill in the blanks with the numbers, separating the periods with commas.<\/div>\n<div data-type=\"problem\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Write a Whole Number Using Digits.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426255684\" class=\"stepwise\" type=\"1\">\n<li>Identify the words that indicate periods. (Remember, the ones period is never named.)<\/li>\n<li>Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\n<li>Name the number in each period and place the digits in the correct place value position.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655200529\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654859177\" data-type=\"problem\">\n<p id=\"fs-id1170655025082\">Write <em data-effect=\"italics\">nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine<\/em> as a whole number using digits.<\/p>\n<\/div>\n<div id=\"fs-id1170655120857\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655190501\">Identify the words that indicate periods.<br \/>\nExcept for the first period, all other periods must have three places. Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.<br \/>\nThen write the digits in each period.<\/p>\n<p><span id=\"fs-id1170655154739\" data-type=\"media\" data-alt=\"An image has two lines of text. The upper lines read \u201cnine billion\u201d, followed by a comma, and \u201ctwo hundred forty six million\u201d, also followed by a comma. The words \u201cbillion\u201d and \u201cmillion\u201d are underlined and each phrase has a curly bracket underneath. The lower lines read \u201cseventy three thousand\u201d, followed by a comma, and \u201cone hundred eighty nine\u201d. The word \u201cthousand\u201d is underlined and each phrase has a curly bracket underneath.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_022_img_new.jpg\" alt=\"An image has two lines of text. The upper lines read \u201cnine billion\u201d, followed by a comma, and \u201ctwo hundred forty six million\u201d, also followed by a comma. The words \u201cbillion\u201d and \u201cmillion\u201d are underlined and each phrase has a curly bracket underneath. The lower lines read \u201cseventy three thousand\u201d, followed by a comma, and \u201cone hundred eighty nine\u201d. The word \u201cthousand\u201d is underlined and each phrase has a curly bracket underneath.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>The number is 9,246,073,189.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655160983\" data-type=\"problem\">\n<p id=\"fs-id1170655162842\">Write the number two billion, four hundred sixty-six million, seven hundred fourteen thousand, fifty-one as a whole number using digits.<\/p>\n<\/div>\n<div id=\"fs-id1170655025046\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655160558\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1b88dab7126cad2f609d0043e5936c1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#44;&#52;&#54;&#54;&#44;&#55;&#49;&#52;&#44;&#48;&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655025845\" data-type=\"problem\">\n<p id=\"fs-id1170655155164\">Write the number eleven billion, nine hundred twenty-one million, eight hundred thirty thousand, one hundred six as a whole number using digits.<\/p>\n<\/div>\n<div id=\"fs-id1170654964907\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654982481\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8a94c1f67e5566abfa8fd50fce0bbebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#44;&#57;&#50;&#49;&#44;&#56;&#51;&#48;&#44;&#49;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>In 2016, Statistics Canada estimated the population of Toronto as 13,448,494. We could say the population of Toronto was approximately 13.4 million. In many cases, you don\u2019t need the exact value; an approximate number is good enough.<\/p>\n<p id=\"fs-id1170655007229\">The process of approximating a number is called <span class=\"no-emphasis\" data-type=\"term\">rounding<\/span>. Numbers are rounded to a specific place value, depending on how much accuracy is needed. Saying that the population of Toronto is approximately 13.4 million means that we rounded to the hundred thousands place.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655027531\" data-type=\"exercise\">\n<div id=\"fs-id1170655120684\" data-type=\"problem\">\n<p id=\"fs-id1170655105094\">Round 23,658 to the nearest hundred.<\/p>\n<\/div>\n<div id=\"fs-id1170655134210\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1170655194626\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains the numbers corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Locate the given place value with an arrow. All digits to the left do not change.\u201d In the the second cell, the instructions say: \u201cLocate the hundreds place in 23,658.\u201d In the third cell, there is the number 23,658 with an arrow pointing to the digit 6, labeling it \u201chundreds place.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains the numbers corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Locate the given place value with an arrow. All digits to the left do not change.\u201d In the the second cell, the instructions say: \u201cLocate the hundreds place in 23,658.\u201d In the third cell, there is the number 23,658 with an arrow pointing to the digit 6, labeling it \u201chundreds place.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655028499\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. Underline the digit to the right of the given place value.\u201d In the second cell, the instructions say: \u201cUnderline the 5, which is to the right of the hundreds place.\u201d In the third cell, there is the number 23,658 again, the same arrow pointing to the digit 6, labeling it the hundreds place. The 5 is also underlined in this cell.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. Underline the digit to the right of the given place value.\u201d In the second cell, the instructions say: \u201cUnderline the 5, which is to the right of the hundreds place.\u201d In the third cell, there is the number 23,658 again, the same arrow pointing to the digit 6, labeling it the hundreds place. The 5 is also underlined in this cell.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654984954\" data-type=\"media\" data-alt=\"One row down, the first cell says: \u201cStep 3. Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do not change the digit in the given place value.\u201d In the second cell, the instructions say: \u201cAdd 1 to the 6 in the hundreds place, since 5 is greater than or equal to 5.\u201d The third cell contains the number 23,658 again, with an arrow pointing at the digit 6 and the text \u201cadd 1\u201d. There is also a curly bracket under the digits 5 and 8, with an arrow pointing at them and the text \u201creplace with 0s.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008c_new.jpg\" alt=\"One row down, the first cell says: \u201cStep 3. Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do not change the digit in the given place value.\u201d In the second cell, the instructions say: \u201cAdd 1 to the 6 in the hundreds place, since 5 is greater than or equal to 5.\u201d The third cell contains the number 23,658 again, with an arrow pointing at the digit 6 and the text \u201cadd 1\u201d. There is also a curly bracket under the digits 5 and 8, with an arrow pointing at them and the text \u201creplace with 0s.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655130142\" data-type=\"media\" data-alt=\"In the bottom row, the first cell says: \u201cStep 4. Replace all digits to the right of the given place value with zeros. So, 23,700 is rounded to the nearest hundred.\u201d In the second cell, the instructions say: \u201cReplace all digits to the right of the hundreds place with zeros.\u201d The third cell contains the number 23,700, which we have reached by rounding the number 23,658 to the nearest hundred.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_008d_new.jpg\" alt=\"In the bottom row, the first cell says: \u201cStep 4. Replace all digits to the right of the given place value with zeros. So, 23,700 is rounded to the nearest hundred.\u201d In the second cell, the instructions say: \u201cReplace all digits to the right of the hundreds place with zeros.\u201d The third cell contains the number 23,700, which we have reached by rounding the number 23,658 to the nearest hundred.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655171044\" data-type=\"problem\">\n<p id=\"fs-id1170655128617\">Round to the nearest hundred: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9bd4e74858116b7d45a7d14895090606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#44;&#56;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654925300\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655108383\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-eb5ed4c560064bb1d605b67147106b80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#44;&#57;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655202716\" data-type=\"problem\">\n<p id=\"fs-id1170655166306\">Round to the nearest hundred: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fd583b5dd38a61c51657eb485ff30e8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;&#56;&#44;&#55;&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654893026\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654863185\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea4aab55035ffaeeb790f4e7b95545cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;&#56;&#44;&#56;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Round Whole Numbers.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426178564\" class=\"stepwise\" type=\"1\">\n<li>Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.<\/li>\n<li>Underline the digit to the right of the given place value.<\/li>\n<li>Is this digit greater than or equal to 5?\n<ul id=\"fs-id1170654989989\" data-bullet-style=\"bullet\">\n<li>Yes\u2013add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e79f5262533d4afca7593790a1c80b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/> to the digit in the given place value.<\/li>\n<li>No\u2013do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\n<\/ul>\n<\/li>\n<li>Replace all digits to the right of the given place value with zeros.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655190444\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655166809\" data-type=\"problem\">\n<p id=\"fs-id1170655151020\">Round <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3095d0fa34e80b4e52274147c9f03547_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#51;&#44;&#57;&#55;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\" \/> to the nearest:<\/p>\n<ol id=\"fs-id1166426039326\" class=\"circled\" type=\"a\">\n<li>hundred<\/li>\n<li>thousand<\/li>\n<li>ten thousand<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1170655106038\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1167835319528\">a)<\/p>\n<table id=\"fs-id1167832055010\" class=\"unnumbered unstyled\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the hundreds place in 103,978.\u201d On the right are the words \u201chundreds place\u201d, followed by an arrow pointing down at the digit 9 in the number 103,978. One row down, the instructions on the left say \u201cUnderline the digit to the right of the hundreds place\u201d. On the right are the words \u201chundreds place\u201d again followed by the same arrow pointing at the digit 9 in 103,978, but the number 7 is also underlined. One row down, the instructions on the left say \u201cSince 7 is greater than or equal to 5, add 1 to the 9. Replace all digits to the right of the hundreds place with zeros.\u201d On the right, the number 103,978 is repeated with the 3 still labeled with the text \u201chundreds place\u201d and the 7 underlined. Another arrow points to the 3 with the text \u201cadd 1; 9 plus 1 equals 10; replace 9 with 0 and carry the 1\u201d. A bracket is drawn underneath the underlined 7 and an arrow points at this bracket with the text \u201creplace with 0s\u201d. One row down, the number 104,000 appears on the right. At the bottom of the image, the text on the left says \u201cSo, 104,000 is 103,978 rounded to the nearest hundred.\u201d\" style=\"width: 100%;\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Locate the hundreds place in 103,978.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167831970141\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Underline the digit to the right of the hundreds place.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167834196335\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Since 7 is greater than or equal to 5, add 1 to the 9. Replace all digits to the right of the hundreds place with zeros.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span id=\"fs-id1167831823617\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\">So, 104,000 is 103,978 rounded to the nearest hundred.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167831894747\">b)<\/p>\n<table id=\"fs-id1167834184013\" class=\"unnumbered unstyled can-break\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the thousands place and underline the digit to the right of the thousands place.\u201d On the right are the words \u201cthousands place\u201d, followed by an arrow pointing down at the digit 3 in the number 103,978. The digit 9 is underlined. One row down, the instructions on the left say \u201cSince 9 is greater than or equal to 5 add 1 to the 3. Replace all digits to the right of the hundreds place with zeros.\u201d On the right, the number 103,978 is repeated with the 3 still labeled with the text \u201cthousands place\u201d and the 9 underlined. Another arrow points to the 3 with the text \u201cadd 1; 3 plus 1 equals 4; replace 3 with 4\u201d. A bracket is drawn underneath the last three digits, 978, and an arrow points at this bracket with the text \u201creplace with 0s\u201d. One row down, the number 104,000 appears on the right. At the bottom of the image, the text on the left says \u201cSo, 104,000 is 103,978 rounded to the nearest thousand.\u201d\" data-label=\"\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>Locate the thousands place and underline the digit to the right of the thousands place.<\/td>\n<td><span id=\"fs-id1167835305151\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Since 9 is greater than or equal to 5, add 1 to the 3. Replace all digits to the right of the hundreds place with zeros.<\/td>\n<td><span id=\"fs-id1167834132960\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So, 104,000 is 103,978 rounded to the nearest thousand.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167832134211\">c)<\/p>\n<table id=\"fs-id1167832006514\" class=\"unnumbered unstyled\" summary=\"This figure contains written instructions on the left and numbers on the right. The first line of instructions in the left column say \u201cLocate the ten thousands place and underline the digit to the right of the ten thousands place.\u201d On the right are the words \u201cten thousands place\u201d, followed by an arrow pointing down at the digit 0 in the number 103,978. The digit 3 is underlined. One row down, the instructions on the left say \u201cSince 0 is less than 5, we leave it as is, and then replace the digits to the right with zeros.\u201d On the right is the number 100,000. At the bottom of the image, the text on the left says \u201cSo, 100,000 is 103,978 rounded to the nearest ten thousand.\u201d\" data-label=\"\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>Locate the ten thousands place and underline the digit to the right of the ten thousands place.<\/td>\n<td>\n<p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f7bbc353e5209483be8d864ab69f6985_l3.png\" height=\"90\" width=\"158\" class=\"ql-img-picture quicklatex-auto-format\" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>Since 3 is less than 5, we leave the 0 as is, and then replace the digits to the right with zeros.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a1eb057c30ec54ff4bf958b6a4a9d02a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bd39041b5d85f208f6cbfa61f4d6691e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>So, 100,000 is 103,978 rounded to the nearest ten thousand.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655154035\" data-type=\"problem\">\n<p id=\"fs-id1170655154263\">Round 206,981 to the nearest: a) hundred b) thousand c) ten thousand.<\/p>\n<\/div>\n<div id=\"fs-id1170655166679\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655074702\">a) 207,000 b) 207,000 c) 210,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655104210\" data-type=\"problem\">\n<p id=\"fs-id1170655025825\">Round 784,951 to the nearest: a) hundred b) thousand c) ten thousand.<\/p>\n<\/div>\n<div id=\"fs-id1170655226376\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655154551\">a) 785,000 b) 785,000 c) 780,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Identify Multiples and Apply Divisibility Tests<\/h1>\n<p id=\"fs-id1170655126540\">The numbers 2, 4, 6, 8, 10, and 12 are called multiples of 2. A multiple of 2 can be written as the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of a counting number and 2<\/p>\n<p><span id=\"fs-id1170655216065\" data-type=\"media\" data-alt=\"A diagram made up of two rows of numbers. The top row reads \u201c2, 4, 6, 8, 10, 12,\u201d followed by an elipsis. Below 2 is 2 times 1, below 4 is 2 times 2, below 6 is 2 times 3, below 8 is 2 times 4, below 10 is 2 times 5, and below 12 is 2 times 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_012_img_new.jpg\" alt=\"A diagram made up of two rows of numbers. The top row reads \u201c2, 4, 6, 8, 10, 12,\u201d followed by an elipsis. Below 2 is 2 times 1, below 4 is 2 times 2, below 6 is 2 times 3, below 8 is 2 times 4, below 10 is 2 times 5, and below 12 is 2 times 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170655163014\">Similarly, a multiple of 3 would be the product of a counting number and 3<\/p>\n<p><span id=\"fs-id1170654944087\" data-type=\"media\" data-alt=\"A diagram made up of two rows of numbers. The top row reads \u201c3, 6, 9, 12, 15, 18,\u201d followed by an elipsis. Below 3 is 3 times 1, below 6 is 3 times 2, below 9 is 3 times 3, below 12 is 3 times 4, below 15 is 3 times 5, and below 18 is 3 times 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_013_img_new.jpg\" alt=\"A diagram made up of two rows of numbers. The top row reads \u201c3, 6, 9, 12, 15, 18,\u201d followed by an elipsis. Below 3 is 3 times 1, below 6 is 3 times 2, below 9 is 3 times 3, below 12 is 3 times 4, below 15 is 3 times 5, and below 18 is 3 times 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170655150368\">We could find the multiples of any number by continuing this process.<\/p>\n<p id=\"fs-id1170654984223\">The <a href=\"#fs-id1170654982162\">Table 1<\/a> below shows the multiples of 2 through 9 for the first 12 counting numbers.<\/p>\n<table id=\"fs-id1170654982162\" class=\"grid\" style=\"height: 176px;width: 100%; width: 100%;\" summary=\"This table has ten rows and thirteen columns. In the first row, which is a header row, the cells read left to right \u201cCounting Number\u201d, \u201c1\u201d, \u201c2\u201d, \u201c3\u201d, \u201c4\u201d, \u201c5\u201d, \u201c6\u201d, \u201c7\u201d, \u201c8\u201d, \u201c9\u201d, \u201c10\u201d, \u201c11\u201d, and \u201c12\u201d. In the second row, the cells read left to right \u201cMultiples of 2\u201d, \u201c2\u201d, \u201c4\u201d, \u201c6\u201d, \u201c8\u201d, \u201c10\u201d, \u201c12\u201d, \u201c14\u201d, \u201c16\u201d, \u201c18\u201d, \u201c20\u201d, \u201c22\u201d, and \u201c24\u201d. In the third row, the cells read left to right, \u201cMultiples of 3\u201d, \u201c3\u201d, \u201c6\u201d, \u201c9\u201d, \u201c12\u201d, \u201c15\u201d, \u201c18\u201d, \u201c21\u201d, \u201c24\u201d, \u201c27\u201d, \u201c30\u201d, \u201c33\u201d, and \u201c36\u201d. In the fourth row, the cells read left to right \u201cMultiples of 4\u201d, \u201c4\u201d, \u201c8\u201d, \u201c12\u201d, \u201c16\u201d, \u201c20\u201d, \u201c24\u201d, \u201c28\u201d, \u201c32\u201d, \u201c36\u201d, \u201c40\u201d, \u201c44\u201d, and \u201c48\u201d. In the fifth row, the cells read left to right \u201cMultiples of 5\u201d, \u201c5\u201d, \u201c10\u201d, \u201c15\u201d, \u201c20\u201d, \u201c25\u201d, \u201c30\u201d, \u201c35\u201d, \u201c40\u201d, \u201c45\u201d, \u201c50\u201d, \u201c55\u201d, and \u201c60\u201d. In the sixth row, the cells read left to right \u201cMultiples of 6\u201d, \u201c6\u201d, \u201c12\u201d, \u201c18\u201d, \u201c24\u201d, \u201c30\u201d,\u201d \u201c36\u201d, \u201c\u201d42\u201d, \u201c48\u201d, \u201c54\u201d, \u201c60\u201d, \u201c66\u201d, and \u201c72\u201d. In the seventh row, the cells read left to right \u201cMultiples of 7\u201d, \u201c7\u201d, \u201c14\u201d, \u201c21\u201d, \u201c28\u201d, \u201c35\u201d, \u201c42\u201d, \u201c49\u201d, \u201c56\u201d, \u201c63\u201d, \u201c70\u201d, \u201c77\u201d, and \u201c84\u201d. In the eighth row, the cells read left to right, \u201cMultiples of 8\u201d, \u201c8\u201d, \u201c16\u201d, \u201c24\u201d, \u201c32\u201d, \u201c40\u201d, \u201c48\u201d, \u201c56\u201d, \u201c64\u201d, \u201c72\u201d, \u201c80\u201d, \u201c88\u201d, and \u201c96\u201d. In the ninth row, the cells read left to right \u201cMultiples of 9\u201d, \u201c9\u201d, \u201c18\u201d, \u201c27\u201d, \u201c36\u201d, \u201c45\u201d, \u201c54\u201d, \u201c63\u201d, \u201c72\u201d, \u201c81\u201d, \u201c90\u201d, \u201c99\u201d, and \u201c108\u201d. In the tenth row, the cells read left to right \u201cMultiples of 10\u201d, \u201c10\u201d, \u201c20\u201d, \u201c30\u201d, \u201c40\u201d, \u201c50\u201d, \u201c60\u201d, \u201c70\u201d, \u201c80\u201d, \u201c90\u201d, \u201c100\u201d, \u201c110\u201d, and \u201c120\u201d.\">\n<caption>Table 1<\/caption>\n<thead>\n<tr style=\"height: 16px\" valign=\"top\">\n<th style=\"height: 16px;width: 67.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">Counting Number<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">1<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">2<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">3<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">4<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">5<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">6<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">7<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">8<\/th>\n<th style=\"height: 16px;width: 16.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">9<\/th>\n<th style=\"height: 16px;width: 25.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">10<\/th>\n<th style=\"height: 16px;width: 24.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">11<\/th>\n<th style=\"height: 16px;width: 25.9062px\" scope=\"col\" data-valign=\"middle\" data-align=\"left\">12<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 2<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">2<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">4<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">14<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">22<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 3<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">3<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">9<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">15<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">21<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">27<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">33<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 4<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">4<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">28<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">32<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">44<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 5<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">5<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">15<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">25<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">35<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">45<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">50<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">55<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 6<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">6<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">12<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">42<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">54<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">66<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 7<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">7<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">14<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">21<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">28<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">35<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">42<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">49<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">56<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">63<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">70<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">77<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">84<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 8<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">8<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">16<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">24<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">32<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">48<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">56<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">64<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">80<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">88<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">96<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 9<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">9<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">18<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">27<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">36<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">45<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">54<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">63<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">72<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">81<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">90<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">99<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">108<\/td>\n<\/tr>\n<tr style=\"height: 16px\" valign=\"top\">\n<td style=\"height: 16px;width: 67.9062px\" data-valign=\"middle\" data-align=\"left\">Multiples of 10<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">10<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">20<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">30<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">40<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">50<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">60<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">70<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">80<\/td>\n<td style=\"height: 16px;width: 16.9062px\" data-valign=\"middle\" data-align=\"left\">90<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">100<\/td>\n<td style=\"height: 16px;width: 24.9062px\" data-valign=\"middle\" data-align=\"left\">110<\/td>\n<td style=\"height: 16px;width: 25.9062px\" data-valign=\"middle\" data-align=\"left\">120<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170655207886\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\" style=\"text-align: left\">Multiple of a Number<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A number is a <strong data-effect=\"bold\">multiple<\/strong> of <em data-effect=\"italics\">n<\/em> if it is the product of a counting number and <em data-effect=\"italics\">n<\/em>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655163445\">Another way to say that 15 is a multiple of 3 is to say that 15 is divisible by 3. That means that when we divide 3 into 15, we get a counting number. In fact, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7862328727a471989e0de9432f4906c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/> is 5, so 15 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c87777a53fbbde38d9de2ad1a049dd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1170655189066\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Divisible by a Number<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If a number <em data-effect=\"italics\">m<\/em> is a multiple of <em data-effect=\"italics\">n<\/em>, then <em data-effect=\"italics\">m<\/em> is <strong data-effect=\"bold\">divisible<\/strong> by <em data-effect=\"italics\">n<\/em>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655229926\">Look at the multiples of 5 in <a class=\"autogenerated-content\" href=\"#fs-id1170654982162\">Table 1<\/a>. They all end in 5 or 0. Numbers with last digit of 5 or 0 are divisible by 5. Looking for other patterns in <a class=\"autogenerated-content\" href=\"#fs-id1170654982162\">Table 1<\/a> that shows multiples of the numbers 2 through 9, we can discover the following divisibility tests:<\/p>\n<div id=\"fs-id1170655221307\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Divisibility Tests<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655202551\">A number is divisible by:<\/p>\n<ul id=\"fs-id1166425936774\" data-bullet-style=\"bullet\">\n<li>2 if the last digit is 0, 2, 4, 6, or 8.<\/li>\n<li>3 if the sum of the digits is divisible by 3.<\/li>\n<li>5 if the last digit is 5 or 0.<\/li>\n<li>6 if it is divisible by both 2 and 3.<\/li>\n<li>10 if it ends with 0.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655205194\" data-type=\"problem\">\n<p id=\"fs-id1170655205196\">Is 5,625 divisible by 2? By 3? By 5? By 6? By 10?<\/p>\n<\/div>\n<div id=\"fs-id1170655229161\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-272\" class=\"unnumbered unstyled\" summary=\".\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>Is 5,625 divisible by 2?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Does it end in 0,2,4,6, or 8?<\/td>\n<td>No.<br \/>\n5,625 is not divisible by 2.<\/td>\n<\/tr>\n<tr>\n<td>Is 5,625 divisible by 3?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>What is the sum of the digits?<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9781d0069db2c1952f7ed7d6474a1944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#54;&#43;&#50;&#43;&#53;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"142\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Is the sum divisible by 3?<\/td>\n<td>Yes. 5,625 is divisble by 3.<\/td>\n<\/tr>\n<tr>\n<td>Is 5,625 divisible by 5 or 10?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>What is the last digit? It is 5.<\/td>\n<td>5,625 is divisble by 5 but not by 10.<\/td>\n<\/tr>\n<tr>\n<td>Is 5,625 divisible by 6?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is it divisible by both 2 or 3?<\/td>\n<td>No, 5,625 is not divisible by 2, so 5,625 is not divisible by 6.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655196872\" data-type=\"problem\">\n<p id=\"fs-id1170655200166\">Determine whether 4,962 is divisible by 2, by 3, by 5, by 6, and by 10<\/p>\n<\/div>\n<div id=\"fs-id1170655200170\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655200173\">by 2, 3, and 6<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655200185\" data-type=\"problem\">\n<p id=\"fs-id1170655200187\">Determine whether 3,765 is divisible by 2, by 3, by 5, by 6, and by 10<\/p>\n<\/div>\n<div id=\"fs-id1170655247400\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655247402\">by 3 and 5<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find Prime Factorization and Least Common Multiples<\/h1>\n<p id=\"fs-id1170655247415\">In mathematics, there are often several ways to talk about the same ideas. So far, we\u2019ve seen that if <em data-effect=\"italics\">m<\/em> is a multiple of <em data-effect=\"italics\">n<\/em>, we can say that <em data-effect=\"italics\">m<\/em> is divisible by <em data-effect=\"italics\">n<\/em>. For example, since 72 is a multiple of 8, we say 72 is divisible by 8. Since 72 is a multiple of 9, we say 72 is divisible by 9. We can express this still another way.<\/p>\n<p id=\"fs-id1170655224271\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e9fe016cd25928ec8712a57509cc0e48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#61;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\" \/>, we say that 8 and 9 are factors of 72. When we write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-05ef2b340ae51e9705915e4c6f4d7716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;&#61;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\" \/>, we say we have factored 72<\/p>\n<p><span id=\"fs-id1170655160732\" data-type=\"media\" data-alt=\"An image shows the equation 8 times 9 equals 72. Written below the expression 8 times 9 is a curly bracket and the word \u201cfactors\u201d while written below 72 is a horizontal bracket and the word \u201cproduct\u201d.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_014_img_new.jpg\" alt=\"An image shows the equation 8 times 9 equals 72. Written below the expression 8 times 9 is a curly bracket and the word \u201cfactors\u201d while written below 72 is a horizontal bracket and the word \u201cproduct\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170655223714\">Other ways to factor 72 are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c1fe263cdf118eba6556d23e6539c046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#50;&#44;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#54;&#44;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#52;&#44;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#56;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"262\" style=\"vertical-align: -4px;\" \/>. Seventy-two has many factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, and 72<\/p>\n<div id=\"fs-id1170655247305\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Factors<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df3ff596a590ca2f84beabbb2a093e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#61;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"68\" style=\"vertical-align: 0px;\" \/>, then <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are factors of <em data-effect=\"italics\">m<\/em>.<\/p>\n<\/div>\n<\/div>\n<p>Some numbers, like 72, have many factors. Other numbers have only two factors.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655269956\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Prime Number and Composite Number<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A <strong>prime number<\/strong> is a counting number greater than 1, whose only factors are 1 and itself.<\/p>\n<p>A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.<\/p>\n<\/div>\n<\/div>\n<p>The counting numbers from 2 to 19 are listed in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_015_img_new\">Figure 4<\/a>, with their factors. Make sure to agree with the \u201cprime\u201d or \u201ccomposite\u201d label for each!<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"CNX_ElemAlg_Figure_01_01_015_img_new\" class=\"bc-figure figure\">\n<figure style=\"width: 881px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_015_img_new.jpg\" alt=\"A table is shown with eleven rows and seven columns. The first row is a header row, and each cell labels the contents of the column below it. In the header row, the first three cells read from left to right \u201cNumber\u201d, \u201cFactors\u201d, and \u201cPrime or Composite?\u201d The entire fourth column is blank. The last three cells read from left to right \u201cNumber\u201d, \u201cFactor\u201d, and \u201cPrime or Composite?\u201d again. In each subsequent row, the first cell contains a number, the second contains its factors, and the third indicates whether the number is prime or composite. The three columns to the left of the blank middle column contain this information for the number 2 through 10, and the three columns to the right of the blank middle column contain this information for the number 11 through 19. On the left side of the blank column, in the first row below the header row, the cells read from left to right: \u201c2\u201d, \u201c1,2\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c3\u201d, \u201c1,3\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c4\u201d, \u201c1,2,4\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c5\u201d, \u201c1,5\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c6\u201d, \u201c1,2,3,6\u201d and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c7\u201d, \u201c1,7\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c8\u201d, \u201c1,2,4,8\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c9\u201d, \u201c1,3,9\u201d, and \u201cComposite\u201d. In the bottom row, the cells read from left to right: \u201c10\u201d, \u201c1,2,5,10\u201d, and \u201cComposite\u201d. On the right side of the blank column, in the first row below the header row, the cells read from left to right: \u201c11\u201d, \u201c1,11\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right: \u201c12\u201d, \u201c1,2,3,4,6,12\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c13\u201d, \u201c1,13\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right \u201c14\u201d, \u201c1,2,7,14\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c15\u201d, \u201c1,3,5,15\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right: \u201c16\u201d, \u201c1,2,4,8,16\u201d, and \u201cComposite\u201d. In the next row, the cells read from left to right, \u201c17\u201d, \u201c1,17\u201d, and \u201cPrime\u201d. In the next row, the cells read from left to right, \u201c18\u201d, \u201c1,2,3,6,9,18\u201d, and \u201cComposite\u201d. In the bottom row, the cells read from left to right: \u201c19\u201d, \u201c1,19\u201d, and \u201cPrime\u201d.\" width=\"881\" height=\"264\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 4<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1170655219626\">The prime number<strong data-effect=\"bold\">s<\/strong> less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Notice that the only even prime number is 2<\/p>\n<p id=\"fs-id1170655205294\">A composite number can be written as a unique <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of primes. This is called the prime factorization of the number. Finding the prime factorization of a composite number will be useful later in this course.<\/p>\n<div id=\"fs-id1170655205301\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Prime Factorization<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The prime factorization of a number is the product of prime numbers that equals the number.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655205314\">To find the prime factorization of a composite number, find any two factors of the number and use them to create two branches. If a factor is prime, that branch is complete. Circle that prime!<\/p>\n<p id=\"fs-id1170655206101\">If the factor is not prime, find two factors of the number and continue the process. Once all the branches have circled primes at the end, the factorization is complete. The composite number can now be written as a product of prime numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">Factor 48.<\/div>\n<div data-type=\"title\"><\/div>\n<div id=\"fs-id1170655206108\" data-type=\"exercise\">\n<div id=\"fs-id1170655206120\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1170655194612\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Find two factors whose product is the given number. Use these numbers to create two branches.\u201d The second cell contains the algebraic equation 48 equals 2 times 24. In the third cell, there is a factor tree with 48 at the top. Two branches descend from 48 and terminate at 2 and 24 respectively.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Find two factors whose product is the given number. Use these numbers to create two branches.\u201d The second cell contains the algebraic equation 48 equals 2 times 24. In the third cell, there is a factor tree with 48 at the top. Two branches descend from 48 and terminate at 2 and 24 respectively.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655105895\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. If a factor is prime, that branch is complete. Circle the prime.\u201d In the second cell, the instructions say: \u201c2 is prime. Circle the prime.\u201d In the third cell, the factor tree from step 1 is repeated, but the 2 at the bottom of the tree is now circled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. If a factor is prime, that branch is complete. Circle the prime.\u201d In the second cell, the instructions say: \u201c2 is prime. Circle the prime.\u201d In the third cell, the factor tree from step 1 is repeated, but the 2 at the bottom of the tree is now circled.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654967999\" data-type=\"media\" data-alt=\"One row down, the first cell says: \u201cStep 3. If a factor is not prime, write it as the product of two factors and continue the process.\u201d In the second cell, the instructions say: \u201c24 is not prime. Break it into 2 more factors.\u201d The third cell contains the original factor tree, with 48 at the top and two downward-pointing branches terminating at 2, which is underlined, and 24. Two more branches descend from 24 and terminate at 4 and 6 respectively. One line down, the instructions in the middle of the cell say \u201c4 and 6 are not prime. Break them each into two factors.\u201d In the cell on the right, the factor tree is repeated once more. Two branches descend from the 4 and terminate at 2 and 2. Both 2s are circled. Two more branches descend from 6 and terminate at a 2 and a 3, which are both circled. The instructions on the left say \u201c2 and 3 are prime, so circle them.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016c_new.jpg\" alt=\"One row down, the first cell says: \u201cStep 3. If a factor is not prime, write it as the product of two factors and continue the process.\u201d In the second cell, the instructions say: \u201c24 is not prime. Break it into 2 more factors.\u201d The third cell contains the original factor tree, with 48 at the top and two downward-pointing branches terminating at 2, which is underlined, and 24. Two more branches descend from 24 and terminate at 4 and 6 respectively. One line down, the instructions in the middle of the cell say \u201c4 and 6 are not prime. Break them each into two factors.\u201d In the cell on the right, the factor tree is repeated once more. Two branches descend from the 4 and terminate at 2 and 2. Both 2s are circled. Two more branches descend from 6 and terminate at a 2 and a 3, which are both circled. The instructions on the left say \u201c2 and 3 are prime, so circle them.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655089548\" data-type=\"media\" data-alt=\"In the bottom row, the first cell says: \u201cStep 4. Write the composite number as the product of all the circled primes.\u201d The second cell is left blank. The third cell contains the algebraic equation 48 equals 2 times 2 times 2 times 2 times 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_016d_new.jpg\" alt=\"In the bottom row, the first cell says: \u201cStep 4. Write the composite number as the product of all the circled primes.\u201d The second cell is left blank. The third cell contains the algebraic equation 48 equals 2 times 2 times 2 times 2 times 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170655194594\">We say <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a164f1634aedd15a228160b60426b1c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" style=\"vertical-align: 0px;\" \/> is the prime factorization of 48. We generally write the primes in ascending order. Be sure to multiply the factors to verify your answer!<\/p>\n<p id=\"fs-id1170655219541\">If we first factored 48 in a different way, for example as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4823b7e39d34e944880202fb0dc55c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, the result would still be the same. Finish the prime factorization and verify this for yourself.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655189533\" data-type=\"problem\">\n<p id=\"fs-id1170655189535\">Find the prime factorization of 80.<\/p>\n<\/div>\n<div id=\"fs-id1170655189540\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655189542\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e7f1b9ac9cc4b2aaf3a6cb5fd15adf69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655206367\" data-type=\"problem\">\n<p id=\"fs-id1170655206369\">Find the prime factorization of 60.<\/p>\n<\/div>\n<div id=\"fs-id1170655206373\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655206375\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0456f31d9d24d834a9cb25b3b58423ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find the Prime Factorization of a Composite Number.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166423940771\" class=\"stepwise\" type=\"1\">\n<li>Find two factors whose product is the given number, and use these numbers to create two branches.<\/li>\n<li>If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.<\/li>\n<li>If a factor is not prime, write it as the product of two factors and continue the process.<\/li>\n<li>Write the composite number as the product of all the circled primes.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655206361\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655206365\" data-type=\"exercise\">\n<div id=\"fs-id1170655206373\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655226116\" data-type=\"problem\">\n<p id=\"fs-id1170655226118\">Find the prime factorization of 252<\/p>\n<\/div>\n<div id=\"fs-id1170655226122\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"fs-id1167834252648\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns with written instructions on the left and a factor tree on the right. The first line of instructions on the left say: \u201cStep 1. Find two factors whose product is 252. 12 and 21 are not prime.\u201d On the right is the top of the factor tree, which starts with 252. Two branches descend from the 252 and terminate at 12 and 21 respectively. On the left, the instructions say \u201cBreak 12 and 21 intwo two more factors. Continue until all primes are factored.\u201d On the right, two branches descend from 21 and terminate at 3 and 7, which are both prime and therefore circled. Two branches also descend from 12 and terminate at 2 and 6 respectively. 2 is prime and therefore circled. Two more branches descend from 6 and terminate at 2 and 3, which are both prime and therefore circled. On the bottom row of the figure, the instructions on the left say: \u201cStep 2. Write 252 as the product of all the circled primes.\u201d On the right is the algebraic equation 252 equals 2 times 2 times 3 times 3 times 7.\" data-label=\"\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">Step 1.<\/strong> Find two factors whose product is 252. 12 and 21 are not prime.<\/p>\n<p>Break 12 and 21 into two more factors. Continue until all primes are factored.<\/td>\n<td><span id=\"fs-id1167835262266\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_017_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 2.<\/strong> Write 252 as the product of all the circled primes.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e56a125132e8ab67c03cd665a2d3132f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#50;&#61;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"146\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655229695\" data-type=\"problem\">\n<p id=\"fs-id1170655229697\">Find the prime factorization of 126<\/p>\n<\/div>\n<div id=\"fs-id1170655229702\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655229704\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-dd2acae66f187c88ceb844ea48fa62a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655270014\" data-type=\"problem\">\n<p id=\"fs-id1170655270016\">Find the prime factorization of 294<\/p>\n<\/div>\n<div id=\"fs-id1170655270020\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655270022\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c13fd659888dfcffe6c3418772a1d4e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655189637\">One of the reasons we look at multiples and primes is to use these techniques to find the least common multiple of two numbers. This will be useful when we add and subtract fractions with different <span class=\"no-emphasis\" data-type=\"term\">denominator<\/span>s. Two methods are used most often to find the least common multiple and we will look at both of them.<\/p>\n<p id=\"fs-id1170655189651\">The first method is the Listing Multiples Method. To find the least common multiple of 12 and 18, we list the first few multiples of 12 and 18:<\/p>\n<p><span id=\"fs-id1170655189662\" data-type=\"media\" data-alt=\"Two rows of numbers are shown. The first row begins with 12, followed by a colon, then 12, 24, 36, 48, 60, 72, 84, 96, 108, and an elipsis. 36, 72, and 108 are bolded written in red. The second row begins with 18, followed by a colon, then 18, 36, 54, 72, 90, 108, and an elipsis. Again, the numbers 36, 72, and 108 are bolded written in red. On the line below is the phrase \u201cCommon Multiples\u201d, a colon and the numbers 36, 72, and 108, written in red. One line below is the phrase \u201cLeast Common Multiple\u201d, a colon and the number 36, written in blue.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_018_img_new.jpg\" alt=\"Two rows of numbers are shown. The first row begins with 12, followed by a colon, then 12, 24, 36, 48, 60, 72, 84, 96, 108, and an elipsis. 36, 72, and 108 are bolded written in red. The second row begins with 18, followed by a colon, then 18, 36, 54, 72, 90, 108, and an elipsis. Again, the numbers 36, 72, and 108 are bolded written in red. On the line below is the phrase \u201cCommon Multiples\u201d, a colon and the numbers 36, 72, and 108, written in red. One line below is the phrase \u201cLeast Common Multiple\u201d, a colon and the number 36, written in blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170655189659\">Notice that some numbers appear in both lists. They are the <strong data-effect=\"bold\">common multiples<\/strong> of 12 and 18<\/p>\n<p id=\"fs-id1170655178513\">We see that the first few common multiples of 12 and 18 are 36, 72, and 108. Since 36 is the smallest of the common multiples, we call it the <em data-effect=\"italics\">least common multiple.<\/em> We often use the abbreviation LCM.<\/p>\n<div id=\"fs-id1170655178531\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Least Common Multiple<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655178544\">The procedure box lists the steps to take to find the LCM using the prime factors method we used above for 12 and 18<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find the Least Common Multiple by Listing Multiples.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1166426329693\" class=\"stepwise\" type=\"1\">\n<li>List several multiples of each number.<\/li>\n<li>Look for the smallest number that appears on both lists.<\/li>\n<li>This number is the LCM.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655178548\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655189105\" data-type=\"problem\">\n<p id=\"fs-id1170655189107\">Find the least common multiple of 15 and 20 by listing multiples.<\/p>\n<\/div>\n<div id=\"fs-id1170655189111\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"fs-id1167831872566\" class=\"unnumbered unstyled can-break\" summary=\"This figure is divided into two coulmns. In the upper left, the instructions say: \u201cMake lists of the first few multiples of 15 and of 20, and use them to find the least common multiple.\u201d The upper right section has two rows of numbers. The first begins with 15 followed by a colon, then 15, 30, 45, 60, 75, 90, 105, and 120. 60 is bolded and written in red. The second row begins with 20 followed by a colon, then 20, 40, 60, 80, 100, 120, 140, and 160. 60 is again bolded and written in red. The lower left section reads \u201cLook for the smallest number that appears in both lists.\u201d The lower right section reads \u201cThe first number to appear on both lists is 60, so 60 is the least common multiple of 15 and 20.\u201d\" data-label=\"\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>Make lists of the first few multiples of 15 and of 20, and use them to find the least common multiple.<\/td>\n<td><span id=\"fs-id1167832051958\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_019_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Look for the smallest number that appears in both lists.<\/td>\n<td>The first number to appear on both lists is 60, so 60 is the least common multiple of 15 and 20.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655206417\">Notice that 120 is in both lists, too. It is a common multiple, but it is not the <em data-effect=\"italics\">least<\/em> common multiple.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655206435\" data-type=\"problem\">\n<p id=\"fs-id1170655206437\">Find the least common multiple by listing multiples: 9 and 12<\/p>\n<\/div>\n<div id=\"fs-id1170655206442\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655206444\">36<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655206456\" data-type=\"problem\">\n<p id=\"fs-id1170655206459\">Find the least common multiple by listing multiples: 18 and 24<\/p>\n<\/div>\n<div id=\"fs-id1170655206463\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655206465\">72<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Our second method to find the least common multiple of two numbers is to use The Prime Factors Method. Let\u2019s find the LCM of 12 and 18 again, this time using their prime factors.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">Find the Least Common Multiple (LCM) of 12 and 18 using the prime factors method.<\/div>\n<div id=\"fs-id1170655199673\" data-type=\"exercise\">\n<div id=\"fs-id1170655199684\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1170655199720\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Write each number as a product of primes.\u201d The second cell is left blank. In the third cell, there are two factor trees. In the first factor tree, two branches descend from 18 and terminate at 3 and 6 respectively. The 3 is prime and therefore circled. Two more branches descend from the 6 and terminate in 2 and 3, both of which are circled. In the second factor tree, two branches descend from 12 and terminate at 3 and 4. The 3 is circled. Two more branches descend from 4, terminating at 2 and 2, both of which are circled.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020a_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions and some math. The third column contains most of the math work corresponding with the written steps and instructions. In the top row, the first cell says: \u201cStep 1. Write each number as a product of primes.\u201d The second cell is left blank. In the third cell, there are two factor trees. In the first factor tree, two branches descend from 18 and terminate at 3 and 6 respectively. The 3 is prime and therefore circled. Two more branches descend from the 6 and terminate in 2 and 3, both of which are circled. In the second factor tree, two branches descend from 12 and terminate at 3 and 4. The 3 is circled. Two more branches descend from 4, terminating at 2 and 2, both of which are circled.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654905180\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cStep 2. List the primes of each number. Match primes vertically when possible.\u201d In the second cell, the instructions say: \u201cList the primes of 12. List the primes of 18. Line up with the primes of 12 when possible. If not create a new column.\u201d The third cell contains the prime factorization of 12 written as the equation 12 equals 2 times 2 times 3. Below this equation is another showing the prime factorization of 18 written as the equation 18 equals 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 in the prime factorization of 12 aligns with the 2 in the prime factorization of 18. Under the second 2 in the prime factorization of 12 is a gap in the prime factorization of 18. Under the 3 in the prime factorization of 12 is the first 3 in the prime factorization of 18. The second 3 in the prime factorization has no factors above it from the prime factorization of 12.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020b_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cStep 2. List the primes of each number. Match primes vertically when possible.\u201d In the second cell, the instructions say: \u201cList the primes of 12. List the primes of 18. Line up with the primes of 12 when possible. If not create a new column.\u201d The third cell contains the prime factorization of 12 written as the equation 12 equals 2 times 2 times 3. Below this equation is another showing the prime factorization of 18 written as the equation 18 equals 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 in the prime factorization of 12 aligns with the 2 in the prime factorization of 18. Under the second 2 in the prime factorization of 12 is a gap in the prime factorization of 18. Under the 3 in the prime factorization of 12 is the first 3 in the prime factorization of 18. The second 3 in the prime factorization has no factors above it from the prime factorization of 12.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655083625\" data-type=\"media\" data-alt=\"One row down, the instructions in the first cell say: \u201cBring down the number from each column.\u201d The second cell is blank. The third cell contains the prime factorizations of 12 and 18 again, illustrated as two equations aligned just as they were before. This time, a horizontal line is drawn under the prime factorization of 18. Below this line is the equation LCM equal to 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 12 through the prime factorization of 18 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 12 and continues down through the 2 in the prime factorization of 18, ending with the first 2 in the LCM. The second arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The third arrow starts at the 3 in the prime factorization of 12 and continues down through the first 3 in the prime factorization of 18, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 18 and points down to the second 3 in the LCM.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020c_new.jpg\" alt=\"One row down, the instructions in the first cell say: \u201cBring down the number from each column.\u201d The second cell is blank. The third cell contains the prime factorizations of 12 and 18 again, illustrated as two equations aligned just as they were before. This time, a horizontal line is drawn under the prime factorization of 18. Below this line is the equation LCM equal to 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 12 through the prime factorization of 18 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 12 and continues down through the 2 in the prime factorization of 18, ending with the first 2 in the LCM. The second arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The third arrow starts at the 3 in the prime factorization of 12 and continues down through the first 3 in the prime factorization of 18, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 18 and points down to the second 3 in the LCM.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654935281\" data-type=\"media\" data-alt=\"In the bottom row of the table, the first cell says: \u201cStep 4: Multiply the factors.\u201d The second cell is bank. The third cell contains the equation LCM equals 36.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_020d_new.jpg\" alt=\"In the bottom row of the table, the first cell says: \u201cStep 4: Multiply the factors.\u201d The second cell is bank. The third cell contains the equation LCM equals 36.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655199709\">Notice that the prime factors of 12 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-80f29661720911230e0cdb3519ba9385_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\" \/> and the prime factors of 18 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a25c09ba790e9fe57002667da848ddad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\" \/> are included in the LCM <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-dd305613ec54b27ff3e7a5a477744a37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/>. So 36 is the least common multiple of 12 and 18<\/p>\n<p id=\"fs-id1170655195905\">By matching up the common primes, each common prime factor is used only once. This way you are sure that 36 is the <em data-effect=\"italics\">least<\/em> common multiple.<\/p>\n<div id=\"fs-id1170655195914\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655195919\" data-type=\"exercise\">\n<div id=\"fs-id1170655195921\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655195921\" data-type=\"problem\">\n<p id=\"fs-id1170655195923\">Find the LCM using the prime factors method: 9 and 12<\/p>\n<\/div>\n<div id=\"fs-id1170655195927\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655195929\">36<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655195942\" data-type=\"problem\">\n<p id=\"fs-id1170655195944\">Find the LCM using the prime factors method: 18 and 24<\/p>\n<\/div>\n<div id=\"fs-id1170655195948\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655195950\">72<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find the Least Common Multiple Using the Prime Factors Method.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426408882\" class=\"stepwise\" type=\"1\">\n<li>Write each number as a product of primes.<\/li>\n<li>List the primes of each number. Match primes vertically when possible.<\/li>\n<li>Bring down the columns.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655229842\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655229887\" data-type=\"problem\">\n<p id=\"fs-id1170655229889\">Find the Least Common Multiple (LCM) of 24 and 36 using the prime factors method.<\/p>\n<\/div>\n<div id=\"fs-id1170655229893\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"fs-id1167826967413\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. The first three lines of instructions on the left say \u201cFind the primes of 24 and 36. Match primes vertically when possible. Bring down all columns.\u201d On the right, the prime factorization of 24 is written as the equation 24 equals 2 times 2 times 2 times 3. Below this equation is another showing the prime factorization of 36 written as the equation 36 equals 2 times 2 times 3 times 3. The two equations line up vertically at the equal symbol. The first 2 and the second 2 in the prime factorization of 24 aligns with the first 2 and the second 2 in the prime factorization of 36. Under the third 2 in the prime factorization of 24 is a gap in the prime factorization of 36. Under the 3 in the prime factorization of 24 is the first 3 in the prime factorization of 36. The second 3 in the prime factorization of 36 has no factors above it from the prime factorization of 24. A horizontal line is drawn under the prime factorization of 36. Below this line is the equation LCM equal to 2 times 2 times 2 times 3 times 3. Arrows are drawn down vertically from the prime factorization of 24 through the prime factorization of 36 ending at the LCM equation. The first arrow starts at the first 2 in the prime factorization of 24 and continues down through the 2 in the prime factorization of 36, ending with the first 2 in the LCM. The second arrow starts at the second 2 in the prime factorization of 24 and continues down through the second 2 in the prime factorization of 36, ending with the second 2 in the LCM. The third arrow starts at the next 2 in the prime factorization of 12 and continues down through the gap in the prime factorization of 18, ending with the second 2 in the LCM. The fourth arrow starts at the 3 in the prime factorization of 24 and continues down through the first 3 in the prime factorization of 36, ending with the first 3 in the LCM. The last arrow starts at the second 3 in the prime factorization of 36 and points down to the second 3 in the LCM. One row down, the instructions on the left say \u201cMultiply the factors.\u201d On the right is the equation LCM equals 72. One line down, on the right, is the text \u201cThe LCM of 24 and 36 is 72.\u201d\" data-label=\"\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>Find the prime factors of 24 and 36.<br \/>\nMatch primes vertically when possible. Bring down all columns.<\/td>\n<td><span id=\"fs-id1167835321942\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply the factors.<\/td>\n<td><span id=\"fs-id1167832116015\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_01_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The LCM of 24 and 36 is 72.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655222007\" data-type=\"problem\">\n<p id=\"fs-id1170655222009\">Find the LCM using the prime factors method: 21 and 28<\/p>\n<\/div>\n<div id=\"fs-id1170655222013\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655222015\">84<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655222028\" data-type=\"problem\">\n<p id=\"fs-id1170655222030\">Find the LCM using the prime factors method: 24 and 32<\/p>\n<\/div>\n<div id=\"fs-id1170655222054\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170655222056\">96<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170655178412\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Place Value<\/strong> as in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_01_002_new\">Figure 2<\/a>.<\/li>\n<li><strong data-effect=\"bold\">Name a Whole Number in Words<\/strong>\n<ol id=\"fs-id1166426408194\" class=\"stepwise\" type=\"1\">\n<li>Start at the left and name the number in each period, followed by the period name.<\/li>\n<li>Put commas in the number to separate the periods.<\/li>\n<li>Do not name the ones period.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Write a Whole Number Using Digits<\/strong>\n<ol id=\"fs-id1166426408220\" class=\"stepwise\" type=\"1\">\n<li>Identify the words that indicate periods. (Remember the ones period is never named.)<\/li>\n<li>Draw 3 blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\n<li>Name the number in each period and place the digits in the correct place value position.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Round Whole Numbers<\/strong>\n<ol id=\"fs-id1166419319557\" class=\"stepwise\" type=\"1\">\n<li>Locate the given place value and mark it with an arrow. All digits to the left of the arrow do not change.<\/li>\n<li>Underline the digit to the right of the given place value.<\/li>\n<li>Is this digit greater than or equal to 5?\n<ul id=\"fs-id1166419319583\" data-bullet-style=\"bullet\">\n<li>Yes\u2014add 1 to the digit in the given place value.<\/li>\n<li>No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\n<\/ul>\n<\/li>\n<li>Replace all digits to the right of the given place value with zeros.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Divisibility Tests:<\/strong> A number is divisible by:\n<ul id=\"fs-id1170655206214\" data-bullet-style=\"open-circle\">\n<li>2 if the last digit is 0, 2, 4, 6, or 8.<\/li>\n<li>3 if the sum of the digits is divisible by 3.<\/li>\n<li>5 if the last digit is 5 or 0.<\/li>\n<li>6 if it is divisible by both 2 and 3.<\/li>\n<li>10 if it ends with 0.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Find the Prime Factorization of a Composite Number<\/strong>\n<ol id=\"fs-id1166423744411\" class=\"stepwise\" type=\"1\">\n<li>Find two factors whose product is the given number, and use these numbers to create two branches.<\/li>\n<li>If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.<\/li>\n<li>If a factor is not prime, write it as the product of two factors and continue the process.<\/li>\n<li>Write the composite number as the product of all the circled primes.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Find the Least Common Multiple by Listing Multiples<\/strong>\n<ol id=\"fs-id1166421706928\" class=\"stepwise\" type=\"1\">\n<li>List several multiples of each number.<\/li>\n<li>Look for the smallest number that appears on both lists.<\/li>\n<li>This number is the LCM.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Find the Least Common Multiple Using the Prime Factors Method<\/strong>\n<ol id=\"fs-id1166421706953\" class=\"stepwise\" type=\"1\">\n<li>Write each number as a product of primes.<\/li>\n<li>List the primes of each number. Match primes vertically when possible.<\/li>\n<li>Bring down the columns.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<dl id=\"fs-id1166424132611\">\n<dd id=\"fs-id1166424132616\">\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166426314283\">\n<dt>composite number<\/dt>\n<dd id=\"fs-id1166426314289\">A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632702\">\n<dt>counting numbers<\/dt>\n<dd id=\"fs-id1166421632707\">The counting numbers are the numbers 1, 2, 3, \u2026<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632717\">\n<dt>divisible by a number<\/dt>\n<dd id=\"fs-id1166421632723\">If a number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8f5290b82f49509335499c00d77889e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a multiple of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5883c3859ac5c6d63005e96eefd4aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8f5290b82f49509335499c00d77889e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is divisible by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5883c3859ac5c6d63005e96eefd4aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>. (If 6 is a multiple of 3, then 6 is divisible by 3.)<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632750\">\n<dt>factors<\/dt>\n<dd id=\"fs-id1166421632755\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f69b1b28ac66a222b016754063ee42c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&middot;&#98;&#61;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8ea6ba93ef998d70cbef6af7e5f297db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/> are factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8f5290b82f49509335499c00d77889e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/>. Since 3 \u00b7 4 = 12, then 3 and 4 are factors of 12.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632812\">\n<dt>least common multiple<\/dt>\n<dd id=\"fs-id1166421632818\">The least common multiple of two numbers is the smallest number that is a multiple of both numbers.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632827\">\n<dt>multiple of a number<\/dt>\n<dd id=\"fs-id1166421632833\">A number is a multiple of <em data-effect=\"italics\">n<\/em> if it is the product of a counting number and <em data-effect=\"italics\">n<\/em>.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632848\">\n<dt>number line<\/dt>\n<dd id=\"fs-id1166421632853\">A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166421632864\">\n<dt>origin<\/dt>\n<dd id=\"fs-id1166421632869\">The origin is the point labeled 0 on a number line.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166424132582\">\n<dt>prime factorization<\/dt>\n<dd id=\"fs-id1166424132587\">The prime factorization of a number is the product of prime numbers that equals the number.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166424132596\">\n<dt>prime number<\/dt>\n<dd id=\"fs-id1166424132602\">A prime number is a counting number greater than 1, whose only factors are 1 and itself.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166424132611\">\n<dt>whole numbers<\/dt>\n<dd id=\"fs-id1166424132616\">The whole numbers are the numbers 0, 1, 2, 3, &#8230;.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use Place Value with Whole Numbers<\/h2>\n<p id=\"fs-id1166421707006\">In the following exercises, find the place value of each digit in the given numbers.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">1. 51,493<br \/>\na) 1<br \/>\nb) 4<br \/>\nc) 9<br \/>\nd) 5<br \/>\ne) 3<\/td>\n<td style=\"width: 50%\">2. 87,210<br \/>\na) 2<br \/>\nb) 8<br \/>\nc) 0<br \/>\nd) 7<br \/>\ne) 1<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">3. 164,285<br \/>\na) 5<br \/>\nb) 6<br \/>\nc) 1<br \/>\nd) 8<br \/>\ne) 2<\/td>\n<td style=\"width: 50%\">4. 395,076<br \/>\na) 5<br \/>\nb) 3<br \/>\nc) 7<br \/>\nd) 0<br \/>\ne) 9<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">5. 93,285,170<br \/>\na) 9<br \/>\nb) 8<br \/>\nc) 7<br \/>\nd) 5<br \/>\ne) 3<\/td>\n<td style=\"width: 50%\">6. 36,084,215<br \/>\na) 8<br \/>\nb) 6<br \/>\nc) 5<br \/>\nd) 4<br \/>\ne) 3<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">7. 7,284,915,860,132<br \/>\na) 7<br \/>\nb) 4<br \/>\nc) 5<br \/>\nd) 3<br \/>\ne) 0<\/td>\n<td style=\"width: 50%\">8. 2,850,361,159,433<br \/>\na) 9<br \/>\nb) 8<br \/>\nc) 6<br \/>\nd) 4<br \/>\ne) 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655227536\">In the following exercises, name each number using words.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 90px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">9. 1,078<\/td>\n<td style=\"width: 50%;height: 15px\">10. 5,902<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">11. 364,510<\/td>\n<td style=\"width: 50%;height: 15px\">12. 146,023<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">13. 5,846,103<\/td>\n<td style=\"width: 50%;height: 15px\">14. 1,458,398<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">15. 37,889,005<\/td>\n<td style=\"width: 50%;height: 15px\">16. 62,008,465<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655206924\">In the following exercises, write each number as a whole number using digits.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 75px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">17. four hundred twelve<\/td>\n<td style=\"width: 50%;height: 15px\">18. two hundred fifty-three<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">19. thirty-five thousand, nine hundred seventy-five<\/td>\n<td style=\"width: 50%;height: 15px\">20. sixty-one thousand, four hundred fifteen<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">21. eleven million, forty-four thousand, one hundred sixty-seven<\/td>\n<td style=\"width: 50%;height: 15px\">22. eighteen million, one hundred two thousand, seven hundred eighty-three<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">23. three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen<\/td>\n<td style=\"width: 50%;height: 15px\">24. eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655194762\">In the following, round to the indicated place value.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194769\">25. Round to the nearest ten.<\/p>\n<p id=\"fs-id1170655194772\">a) 386 b) 2,931<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194788\">26. Round to the nearest ten.<\/p>\n<p id=\"fs-id1170655194792\">a) 792 b) 5,647<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194808\">27. Round to the nearest hundred.<\/p>\n<p id=\"fs-id1170655194811\">a) 13,748 b) 391,794<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194827\">28. Round to the nearest hundred.<\/p>\n<p id=\"fs-id1170655194830\">a) 28,166 b) 481,628<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194846\">29. Round to the nearest ten.<\/p>\n<p id=\"fs-id1170655194849\">a) 1,492 b) 1,497<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194865\">30. Round to the nearest ten.<\/p>\n<p id=\"fs-id1170655194869\">a) 2,791 b) 2,795<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194886\">31. Round to the nearest hundred.<\/p>\n<p id=\"fs-id1170655194889\">a) 63,994 b) 63,940<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170655194906\">32. Round to the nearest hundred.<\/p>\n<p id=\"fs-id1170655194910\">a) 49,584 b) 49,548<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655198323\">In the following exercises, round each number to the nearest a) hundred, b) thousand, c) ten thousand.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">33. 392,546<\/td>\n<td style=\"width: 50%\">34. 619,348<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">35. 2,586,991<\/td>\n<td style=\"width: 50%\">36. 4,287,965<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Identify Multiples and Factors<\/h2>\n<p id=\"fs-id1170655198399\">In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 120px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">37. 84<\/td>\n<td style=\"width: 50%;height: 15px\">38. 9,696<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">39. 75<\/td>\n<td style=\"width: 50%;height: 15px\">40. 78<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">41. 900<\/td>\n<td style=\"width: 50%;height: 15px\">42. 800<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">43. 986<\/td>\n<td style=\"width: 50%;height: 15px\">44. 942<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">45. 350<\/td>\n<td style=\"width: 50%;height: 15px\">46. 550<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">47. 22,335<\/td>\n<td style=\"width: 50%;height: 15px\">48. 39,075<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Find Prime Factorizations and Least Common Multiples<\/h2>\n<p id=\"fs-id1170655196091\">In the following exercises, find the prime factorization.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 121px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">49. 86<\/td>\n<td style=\"width: 50%;height: 16px\">50. 78<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">51. 132<\/td>\n<td style=\"width: 50%;height: 15px\">52. 455<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">53. 693<\/td>\n<td style=\"width: 50%;height: 15px\">54. 400<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">55. 432<\/td>\n<td style=\"width: 50%;height: 15px\">56. 627<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">57. 2,160<\/td>\n<td style=\"width: 50%;height: 15px\">58. 2,520<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655165795\">In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">59. 8, 12<\/td>\n<td style=\"width: 50%\">60. 4, 3<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">61. 12, 16<\/td>\n<td style=\"width: 50%\">62. 30, 40<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">63. 20, 30<\/td>\n<td style=\"width: 50%\">64. 44, 55<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655170829\">In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">65. 8, 12<\/td>\n<td style=\"width: 50%\">66. 12, 16<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">67. 28, 40<\/td>\n<td style=\"width: 50%\">68. 84, 90<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">69. 55, 88<\/td>\n<td style=\"width: 50%\">70. 60, 72<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse;width: 100%;height: 106px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">71. <strong data-effect=\"bold\">Writing a Check<\/strong> Jorge bought a car for &#36;24,493. He paid for the car with a check. Write the purchase price in words.<\/td>\n<td style=\"width: 50%;height: 16px\">72. <strong data-effect=\"bold\">Writing a Check<\/strong> Marissa\u2019s kitchen remodeling cost &#36;18,549. She wrote a check to the contractor. Write the amount paid in words.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">73. <strong data-effect=\"bold\">Buying a Car<\/strong> Jorge bought a car for &#36;24,493. Round the price to the nearest a) ten b) hundred c) thousand; and d) ten-thousand.<\/td>\n<td style=\"width: 50%;height: 15px\">74. <strong data-effect=\"bold\">Remodeling a Kitchen<\/strong> Marissa\u2019s kitchen remodeling cost &#36;18,549, Round the cost to the nearest a) ten b) hundred c) thousand and d) ten-thousand.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">75. <strong data-effect=\"bold\">Population<\/strong> The population of China was 1,339,724,852 on November 1, 2010. Round the population to the nearest a) billion b) hundred-million; and c) million.<\/td>\n<td style=\"width: 50%;height: 15px\">76. <strong data-effect=\"bold\">Astronomy<\/strong> The average distance between Earth and the sun is 149,597,888 kilometres. Round the distance to the nearest a) hundred-million b) ten-million; and c) million.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">77. <strong data-effect=\"bold\">Grocery Shopping<\/strong> Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?<\/td>\n<td style=\"width: 50%;height: 15px\">78. <strong data-effect=\"bold\">Grocery Shopping<\/strong> Paper plates are sold in packages of 12 and party cups come in packs of eight. What is the smallest number that makes the plates and cups come out even?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">79. What is the difference between prime numbers and composite numbers?<\/td>\n<td style=\"width: 50%\">80. Give an everyday example where it helps to round numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">81. Explain in your own words how to find the prime factorization of a composite number, using any method you prefer.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/dd>\n<\/dl>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse;width: 100%;height: 310px\">\n<tbody>\n<tr style=\"height: 35px\">\n<td style=\"width: 33.3333%;height: 35px\">1. a) thousands b) hundreds c) tens d) ten thousands e) ones<\/td>\n<td style=\"width: 33.3333%;height: 35px\">3. a) ones b) ten thousands c) hundred thousands d) tens e) hundreds<\/td>\n<td style=\"width: 33.3333%;height: 35px\">5. a) ten millions b) ten thousands c) tens d) thousands e) millions<\/td>\n<\/tr>\n<tr style=\"height: 35px\">\n<td style=\"width: 33.3333%;height: 35px\">7. a) trillions b) billions c) millions d) tens e) thousands<\/td>\n<td style=\"width: 33.3333%;height: 35px\">9. one thousand, seventy-eight<\/td>\n<td style=\"width: 33.3333%;height: 35px\">11. three hundred sixty-four thousand, five hundred ten<\/td>\n<\/tr>\n<tr style=\"height: 35px\">\n<td style=\"width: 33.3333%;height: 35px\">13. five million, eight hundred forty-six thousand, one hundred three<\/td>\n<td style=\"width: 33.3333%;height: 35px\">15. thirty-seven million, eight hundred eighty-nine thousand, five<\/td>\n<td style=\"width: 33.3333%;height: 35px\">17. 412<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">19. 35,975<\/td>\n<td style=\"width: 33.3333%;height: 17px\">21. 11,044,167<\/td>\n<td style=\"width: 33.3333%;height: 17px\">23. 3,226,512,017<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">25. a) 390 b) 2,930<\/td>\n<td style=\"width: 33.3333%;height: 17px\">27. a) 13,700 b) 391,800<\/td>\n<td style=\"width: 33.3333%;height: 17px\">29. a) 1,490 b) 1,500<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">31. a) 64,000 b) 63,900<\/td>\n<td style=\"width: 33.3333%;height: 17px\">33. a) 392,500 b) 393,000 c) 390,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">35. a) 2,587,000 b) 2,587,000 c) 2,590,000<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">37. divisible by 2, 3, and 6<\/td>\n<td style=\"width: 33.3333%;height: 17px\">39. divisible by 3 and 5<\/td>\n<td style=\"width: 33.3333%;height: 17px\">41. divisible by 2, 3, 5, 6, and 10<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">43. divisible by 2<\/td>\n<td style=\"width: 33.3333%;height: 17px\">45. divisible by 2, 5, and 10<\/td>\n<td style=\"width: 33.3333%;height: 17px\">47. divisible by 3 and 5<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-18ee52e9351dbeee99229dd6a736ddfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-407128fedcd2ea014310f70cdae69a32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0462664b74c0539bdc00a5f098f2eb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"82\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-622b2858b3e178f3e8c1ec5bcdc32871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"139\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bf515ccb24bbb6119e947b3a313dc096_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"160\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">59. 24<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">61. 48<\/td>\n<td style=\"width: 33.3333%;height: 17px\">63. 60<\/td>\n<td style=\"width: 33.3333%;height: 17px\">65. 24<\/td>\n<\/tr>\n<tr style=\"height: 35px\">\n<td style=\"width: 33.3333%;height: 35px\">67. 280<\/td>\n<td style=\"width: 33.3333%;height: 35px\">69. 440<\/td>\n<td style=\"width: 33.3333%;height: 35px\">71. twenty-four thousand, four hundred ninety-three dollars<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">73. a) &#36;24,490 b) &#36;24,500 c) &#36;24,000 d) &#36;20,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">75. a) 1,000,000,000 b) 1,300,000,000 c) 1,340,000,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">77. 40<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">79. Answers may vary.<\/td>\n<td style=\"width: 33.3333%;height: 17px\">81. Answers may vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cIntroduction to Whole Numbers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n<p><!-- pb_fixme --><\/p>\n","protected":false},"author":999,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-55","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":20,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/55","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/55\/revisions"}],"predecessor-version":[{"id":4121,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/55\/revisions\/4121"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/55\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/media?parent=55"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapter-type?post=55"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/contributor?post=55"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/license?post=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}