Unit 2: Division
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
Answers to Exercise 1
The following numbers are divisible by 2: a, d, e, h, j, k.
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 three, so 63 is divisible by three.
Example D
148
1 + 4 + 8 = 13
13 is not divisible by three, 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
Answers to Exercise 2
The following numbers are divisible by 3: a, c, g, j, k.
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 3
The following numbers are divisible by 5: a, d, e, h, j, k.
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: b, c, f, g, j, k
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 | ||||
210 |
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 |
210 | Yes | Yes | Yes | No |
Exercise 8
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 |
---|---|---|---|---|
837 | ||||
360 | ||||
648 | ||||
981 | ||||
465 | ||||
1002 | ||||
3520 | ||||
6435 | ||||
8022 | ||||
7425 |
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 |
7425 | No | Yes | Yes | Yes |
Exercise 9
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 |
---|---|---|---|---|
1200 | ||||
7164 | ||||
3681 | ||||
8205 | ||||
2745 | ||||
4320 | ||||
7350 | ||||
4000 | ||||
1368 | ||||
6720 |
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 |
6720 | Yes | Yes | Yes | No |
Topic B: Self-Test
Mark /12 Aim 9/12
- From the list of numbers, write the numbers that are divisible by the specified number.
48, 925, 1467, 2645, 5534, 7512, 31183, 52361- Which numbers are divisible by 2?
- Which numbers are divisible by 3?
- Which numbers are divisible by 5?
- Which numbers are divisible by 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
Answers to Topic B Self-Test
- From the list of numbers, write the numbers that are divisible by the specified number.
- 48, 7512, 5534
- 48, 1467, 7512
- 925, 2645
- 1467
- 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