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 | |