1.10: Divisibility

For example, 18 is divisible by 3 because [latex]18 \div 3 = 6[/latex]. 18 is not divisible by 5 because [latex]18 \div 5 = 3[/latex] 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.

  1. 22
  2. 35
  3. 17
  4. 10
  5. 274
  6. 345
  7. 639
  8. 456
  9. 2437
  10. 7548
  11. 6754
  12. 5543

Exercise 1 Answers

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

[latex]6 + 3 = 9[/latex]

9 is divisible by three, so 63 is divisible by three.

Example D

148

[latex]1 + 4 + 8 = 13[/latex]

13 is not divisible by three, so 148 is not divisible by 3.

Example E

5892

[latex]5 + 8 + 9 + 2 = 24[/latex]

Add again:

[latex]2 + 4 = 6[/latex]

6 is divisible by 3, so 5892 is divisible by 3.

Exercise 2

Circle the numbers that are divisible by 3.

  1. 27
  2. 35
  3. 81
  4. 94
  5. 274
  6. 581
  7. 564
  8. 316
  9. 3175
  10. 1458
  11. 1890
  12. 3934

Exercise 2 Answers

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.

  1. 45
  2. 84
  3. 72
  4. 90
  5. 800
  6. 753
  7. 672
  8. 355
  9. 6009
  10. 6375
  11. 7020
  12. 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.

  1. 474
  2. 615
  3. 412
  4. 865
  5. 300
  6. 831
  7. 525
  8. 350
  9. 710
  10. 429
  11. 906
  12. 634
  13. 430
  14. 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.

  1. 3585
  2. 7548
  3. 5890
  4. 6318
  5. 3905
  6. 5280
  7. 1760
  8. 8007
  9. 6752
  10. 7375
  11. 5523
  12. 2625
  13. 8956
  14. 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.

Divisibility by 9

A number is divisible by 9 if the sum (total) of the digits is divisible by 9.

Example H

135

[latex]1 + 3 + 5 = 9[/latex]

9 is divisible by 9, so 135 is divisible by 9.

Example I

7578

[latex]7 + 5 + 7 + 8 = 27[/latex]

27 is divisible by 9, so 7578 is divisible by 9.

Example J

57896

[latex]5 + 7 + 8 + 9 + 6 = 35[/latex]

35 is not divisible by 9, so 57896 is not divisible by 9.

Exercise 6

Circle the numbers that are divisible by 9.

  1. 538
  2. 783
  3. 954
  4. 762
  5. 6213
  6. 5742
  7. 7083
  8. 5738
  9. 34937
  10. 39402
  11. 74124
  12. 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.

  1. 453
  2. 320
  3. 216
  4. 726
  5. 712
  6. 425
  7. 630
  8. 375
  9. 990
  10. 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.

  1. 837
  2. 360
  3. 648
  4. 981
  5. 465
  6. 1002
  7. 3520
  8. 6435
  9. 8022
  10. 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.

  1. 1200
  2. 7164
  3. 3681
  4. 8205
  5. 2745
  6. 4320
  7. 7350
  8. 4000
  9. 1368
  10. 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.

1.10: Practice Questions

  1. From the list of numbers, write the numbers that are divisible by the specified number.
    48, 925, 1467, 2645, 5534, 7512, 31183, 52361

    1. Which numbers are divisible by 2?
    2. Which numbers are divisible by 3?
    3. Which numbers are divisible by 5?
    4. Which numbers are divisible by 9?

     

  2. For each number, identify if it is divisible by 2, 3, 5, and 9.
    1. 1200
    2. 7164
    3. 3681
    4. 8205
    5. 2745

1.10: Practice Answers

  1. From the list of numbers, write the numbers that are divisible by the specified number.
    1. 48, 7512, 5534
    2. 48, 1467, 7512
    3. 925, 2645
    4. 1467

     

  2. 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.

Attribution

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.

License

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Intermediate PreAlgebra: Building Success Copyright © 2024 by Kim Tamblyn, TRU Open Press is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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