Topic B: Divisibility
Divisibility is when two numbers can be divided without a remainder.
For example, 18 is divisible by 3 because 18 ÷ 3 = 6.
18 is not divisible by 5 because 18 ÷ 5 = 3 with a remainder of 3.
Divisibility by 2
A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8.
Example A
438, 540, 256, 12, and 154 are all divisible by 2 because each number ends in a 0, 2, 4, 6, or 8.
Example B
351, 945, 849, 347, and 193 are not divisible by 2 because each number does not end in a 0, 2, 4, 6 or 8.
Exercise 1
Circle the numbers that are divisible by 2. Check your work using the answer key at the end of the exercise.
- 22
- 35
- 17
- 10
- 274
- 345
- 639
- 456
- 2437
- 7548
- 6754
- 5543
Divisibility by 3
A number is divisible by 3 if the sum (total) of the digits is divisible by 3.
Example C
63
6 + 3 = 9
9 is divisible by 3, so 63 is divisible by 3.
Example D
148
1 + 4 + 8 = 13
13 is not divisible by 3, so 148 is not divisible by 3.
Example E
5892
5 + 8 + 9 + 2 = 24
Add again: 2 + 4 = 6
6 is divisible by 3, so 5892 is divisible by 3.
Exercise 2
Circle the numbers that are divisible by 3. Check your work using the answer key at the end of the exercise.
- 27
- 35
- 81
- 94
- 274
- 581
- 564
- 316
- 3175
- 1458
- 1890
- 3934
Divisibility by 5
A number is divisible by 5 if the number ends in 0 or 5.
Example F
290 is divisible by 5 because it ends in 0.
Example G
132 is not divisible by 5 because it does not end in 0 or 5.
Exercise 3
Circle the numbers that are divisible by 5. Check your work using the answer key at the end of the exercise.
- 45
- 84
- 72
- 90
- 800
- 753
- 672
- 355
- 6009
- 6375
- 7020
- 1704
Answers to Exercise 1
The following numbers are divisible by 2: 22, 10, 274, 456, 7 548, 6 754.
Answers to Exercise 2
The following numbers are divisible by 3: 27, 81, 564, 1 458, 3 175, 1 890.
Answers to Exercise 3
The following numbers are divisible by 5: 45, 90, 800, 355, 6 375, 7 020.
Exercise 4
For each number, identify if it is divisible by 2, 3, and 5. Check your work using the answer key at the end of the exercise.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 |
|---|---|---|---|
| 474 | Yes | Yes | No |
| 615 | |||
| 412 | |||
| 865 | |||
| 300 | |||
| 831 | |||
| 525 | |||
| 350 | |||
| 710 | |||
| 429 | |||
| 906 | |||
| 634 | |||
| 430 | |||
| 275 |
Answers to Exercise 4
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 |
|---|---|---|---|
| 474 | Yes | Yes | No |
| 615 | No | Yes | Yes |
| 412 | Yes | No | No |
| 865 | No | No | Yes |
| 300 | Yes | Yes | Yes |
| 831 | No | Yes | No |
| 525 | No | Yes | Yes |
| 350 | Yes | No | Yes |
| 710 | Yes | No | Yes |
| 429 | No | Yes | No |
| 906 | Yes | Yes | No |
| 634 | Yes | No | No |
| 430 | Yes | No | Yes |
| 275 | No | No | Yes |
Exercise 5
For each number, identify if it is divisible by 2, 3, and 5. Check your work using the answer key at the end of the exercise.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 |
|---|---|---|---|
| 3585 | |||
| 7548 | |||
| 5890 | |||
| 6318 | |||
| 3905 | |||
| 5280 | |||
| 1760 | |||
| 8007 | |||
| 6752 | |||
| 7375 | |||
| 5523 | |||
| 2625 | |||
| 8956 | |||
| 9150 |
Answers to Exercise 5
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 |
|---|---|---|---|
| 3585 | No | Yes | Yes |
| 7548 | Yes | Yes | No |
| 5890 | Yes | No | Yes |
| 6318 | Yes | Yes | No |
| 3905 | No | No | Yes |
| 5280 | Yes | Yes | Yes |
| 1760 | Yes | No | Yes |
| 8007 | No | Yes | No |
| 6752 | Yes | No | No |
| 7375 | No | No | Yes |
| 5523 | No | Yes | No |
| 2625 | No | Yes | Yes |
| 8956 | Yes | No | No |
| 9150 | Yes | Yes | Yes |
Divisibility by 9
A number is divisible by 9 if the sum (total) of the digits is divisible by 9.
Example H
135
1 + 3 + 5 = 9
9 is divisible by 9, so 135 is divisible by 9.
Example I
7578
7 + 5 + 7 + 8 = 27
27 is divisible by 9, so 7578 is divisible by 9.
Example J
57896
5 + 7 + 8 + 9 + 6 = 35
35 is not divisible by 9, so 57896 is not divisible by 9.
Exercise 6
Circle the numbers that are divisible by 9. Check your work using the answer key at the end of the exercise.
- 538
- 783
- 954
- 762
- 6213
- 5742
- 7083
- 5738
- 34937
- 39402
- 74124
- 45683
Answers to Exercise 6
The following numbers are divisible by 9: 783, 954, 5 742, 7 083, 39 402, 74 124.
Exercise 7
For each number, identify if it is divisible by 2, 3, 5, and 9. Check your work using the answer key at the end of the exercise.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 453 | ||||
| 320 | ||||
| 216 | ||||
| 726 | ||||
| 712 | ||||
| 425 | ||||
| 630 | ||||
| 375 | ||||
| 990 |
Answers to Exercise 7
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 453 | No | Yes | No | No |
| 320 | Yes | No | Yes | No |
| 216 | Yes | Yes | No | Yes |
| 726 | Yes | Yes | No | No |
| 712 | Yes | No | No | No |
| 425 | No | No | Yes | No |
| 630 | Yes | Yes | Yes | Yes |
| 375 | No | Yes | Yes | No |
| 990 | Yes | Yes | Yes | Yes |
Exercise 8
For each number, identify if it is divisible by 2, 3, 5, and 9.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 837 | ||||
| 360 | ||||
| 648 | ||||
| 981 | ||||
| 465 | ||||
| 1002 | ||||
| 3520 | ||||
| 6435 | ||||
| 8022 |
Answers to Exercise 8
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 837 | No | Yes | No | Yes |
| 360 | Yes | Yes | Yes | Yes |
| 648 | Yes | Yes | No | Yes |
| 981 | No | Yes | No | Yes |
| 465 | No | Yes | Yes | No |
| 1002 | Yes | Yes | No | No |
| 3520 | Yes | No | Yes | No |
| 6435 | No | Yes | Yes | Yes |
| 8022 | Yes | Yes | No | No |
Exercise 9
For each number, identify if it is divisible by 2, 3, 5, and 9.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 1200 | ||||
| 7164 | ||||
| 3681 | ||||
| 8205 | ||||
| 2745 | ||||
| 4320 | ||||
| 7350 | ||||
| 4000 | ||||
| 1368 |
Answers to Exercise 9
| Number | Divisible by 2 | Divisible by3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 1200 | Yes | Yes | Yes | No |
| 7164 | Yes | Yes | No | Yes |
| 3681 | No | Yes | No | Yes |
| 8205 | No | Yes | Yes | No |
| 2745 | No | Yes | Yes | Yes |
| 4320 | Yes | Yes | Yes | Yes |
| 7350 | Yes | Yes | Yes | No |
| 4000 | Yes | No | Yes | No |
| 1368 | Yes | Yes | No | Yes |
Topic B: Self-Test
Mark /12 Aim 9/12
A. From the list of numbers, write the numbers that are divisible by the specified number.
- Which numbers are divisible by 2?
- Which numbers are divisible by 3?
- Which numbers are divisible by 5?
- Which numbers are divisible by 9?
B. For each number, identify if it is divisible by 2, 3, 5, and 9.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 1200 | ||||
| 7164 | ||||
| 3681 | ||||
| 8205 | ||||
| 2745 |
Answers to Topic B Self Test
A. From the list of numbers, write the numbers that are divisible by the specified number.
- 48, 7512, 5534
- 48, 1467, 7512
- 925, 2645
- 1467
B. For each number, identify if it is divisible by 2, 3, 5, and 9.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 9 |
|---|---|---|---|---|
| 1200 | Yes | Yes | Yes | No |
| 7164 | Yes | Yes | No | Yes |
| 3681 | No | Yes | No | Yes |
| 8205 | No | Yes | Yes | No |
| 2745 | No | Yes | Yes | Yes |