1.10: Divisibility
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.
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
Exercise 1 Answers
The following numbers are divisible by 2: a, d, e, h, j, k.
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.
- 27
- 35
- 81
- 94
- 274
- 581
- 564
- 316
- 3175
- 1458
- 1890
- 3934
Exercise 2 Answers
The following numbers are divisible by 3: a, c, g, j, k.
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.
- 45
- 84
- 72
- 90
- 800
- 753
- 672
- 355
- 6009
- 6375
- 7020
- 1704
Exercise 3 Answers
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.
- 474
- 615
- 412
- 865
- 300
- 831
- 525
- 350
- 710
- 429
- 906
- 634
- 430
- 275
Exercise 4 Answers
- Divisible by 2: a, c, e, h, i, k, l, m.
- Divisible by 3: a, b, e, f, g, j, k.
- Divisible by 5: b, d, e, g, h, i, m, n.
Exercise 5
For each number, identify if it is divisible by 2, 3, and 5.
- 3585
- 7548
- 5890
- 6318
- 3905
- 5280
- 1760
- 8007
- 6752
- 7375
- 5523
- 2625
- 8956
- 9150
Exercise 5 Answers
- Divisible by 2: b, c, d, f, g, i, m, n.
- Divisible by 3: a, b, d, f, h, k, l, n.
- Divisible by 5: a, c, e, f, g, j, l, n.
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.
- 538
- 783
- 954
- 762
- 6213
- 5742
- 7083
- 5738
- 34937
- 39402
- 74124
- 45683
Exercise 6 Answers
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.
- 453
- 320
- 216
- 726
- 712
- 425
- 630
- 375
- 990
- 210
Exercise 7 Answers
- Divisible by 2: b, c, d, e, g, i, j.
- Divisible by 3: a, c, d, g, h, i, j.
- Divisible by 5: b, f, g, h, i, j.
- Divisible by 9: c, g, i.
Exercise 8
For each number, identify if it is divisible by 2, 3, 5, and 9.
- 837
- 360
- 648
- 981
- 465
- 1002
- 3520
- 6435
- 8022
- 7425
Exercise 8 Answers
- Divisible by 2: b, c, f, g, i.
- Divisible by 3: a, b, c, d, f, h, i, j.
- Divisible by 5: b, e, g, h, j
- Divisible by 9: a, b, c, d, h, j.
Exercise 9
For each number, identify if it is divisible by 2, 3, 5, and 9.
- 1200
- 7164
- 3681
- 8205
- 2745
- 4320
- 7350
- 4000
- 1368
- 6720
Exercise 9 Answers
- Divisible by 2: a, b, f, g, h, i, j.
- Divisible by 3: a, b, c, d, e, f, g, i, j.
- Divisible by 5: a, d, e, f, g, h, j.
- Divisible by 9: b, c, e, f, i.
- 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.
- 1200
- 7164
- 3681
- 8205
- 2745
1.10: Practice Answers
- 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.
- Divisible by 2: a, b.
- Divisible by 3: a, b, c, d, e.
- Divisible by 5: a, d, e.
- Divisible by 9: b, c, e.
This chapter has been adapted from Topic B: Divisibility in Adult Literacy Fundamental Mathematics: Book 3 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard (2023), which is under a CC BY 4.0 license.
