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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 304 · 40 questions
TalentJR

The method (Rules and powers): By 3 or 9: the digit sum divides by 3 or 9. By 4: the last two digits. By 8: the last three digits. By 6: even and divisible by 3. By 11: the sums of alternate digits are equal or differ by 11. Number of factors: write n = p^a × q^b …, then the count is (a + 1) × (b + 1) × …. To make n divisible by d: divide, then add (d − remainder) or take away the remainder.

NameDateTime takenScore ___ / 40
  1. 1.Which of these numbers divides exactly by 6? (a) 8832 (b) 9308 (c) 4879 (d) 7615
  2. 2.Which of these numbers divides exactly by 6? (a) 8747 (b) 4218 (c) 3283 (d) 5055
  3. 3.How many factors does 37 have?
  4. 4.How many factors does 97 have?
  5. 5.What is the smallest number you must add to 955 so that it divides exactly by 13?
  6. 6.What is the smallest number you must add to 482 so that it divides exactly by 7?
  7. 7.Which of these numbers divides exactly by 11? (a) 8076 (b) 5082 (c) 9333 (d) 7489
  8. 8.How many factors does 94 have?
  9. 9.Which of these numbers divides exactly by 8? (a) 5609 (b) 3203 (c) 7117 (d) 5232
  10. 10.How many factors does 35 have?
  11. 11.How many factors does 86 have?
  12. 12.Which of these numbers divides exactly by 8? (a) 2185 (b) 1248 (c) 3502 (d) 5266
  13. 13.What is the smallest number you must take away from 766 so that it divides exactly by 3?
  14. 14.What is the smallest number you must take away from 217 so that it divides exactly by 6?
  15. 15.What is the smallest number you must take away from 617 so that it divides exactly by 12?
  16. 16.What is the smallest number you must add to 821 so that it divides exactly by 3?
  17. 17.How many factors does 78 have?
  18. 18.What is the smallest number you must add to 582 so that it divides exactly by 8?
  19. 19.How many factors does 80 have?
  20. 20.Which of these numbers divides exactly by 11? (a) 4749 (b) 5178 (c) 3129 (d) 2332
  21. 21.What is the smallest number you must take away from 747 so that it divides exactly by 11?
  22. 22.Which of these numbers divides exactly by 11? (a) 5102 (b) 4403 (c) 2751 (d) 5357
  23. 23.What is the smallest number you must add to 968 so that it divides exactly by 13?
  24. 24.What is the smallest number you must take away from 628 so that it divides exactly by 11?
  25. 25.How many factors does 61 have?
  26. 26.What is the smallest number you must add to 849 so that it divides exactly by 4?
  27. 27.What is the smallest number you must add to 277 so that it divides exactly by 6?
  28. 28.Which of these numbers divides exactly by 4? (a) 1886 (b) 9879 (c) 6066 (d) 7872
  29. 29.Which of these numbers divides exactly by 11? (a) 9425 (b) 1902 (c) 1191 (d) 5797
  30. 30.How many factors does 40 have?
  31. 31.Which of these numbers divides exactly by 11? (a) 2983 (b) 7678 (c) 3866 (d) 7596
  32. 32.Which of these numbers divides exactly by 3? (a) 3931 (b) 9680 (c) 5604 (d) 4670
  33. 33.Which of these numbers divides exactly by 9? (a) 2461 (b) 5531 (c) 7684 (d) 1701
  34. 34.How many factors does 38 have?
  35. 35.How many factors does 13 have?
  36. 36.What is the smallest number you must add to 884 so that it divides exactly by 12?
  37. 37.What is the smallest number you must add to 334 so that it divides exactly by 6?
  38. 38.How many factors does 84 have?
  39. 39.How many factors does 18 have?
  40. 40.What is the smallest number you must take away from 191 so that it divides exactly by 7?

Answer key

  1. 8832
  2. 4218
  3. 2
  4. 2
  5. 7
  6. 1
  7. 5082
  8. 4
  9. 5232
  10. 4
  11. 4
  12. 1248
  13. 1
  14. 1
  15. 5
  16. 1
  17. 8
  18. 2
  19. 10
  20. 2332
  21. 10
  22. 5357
  23. 7
  24. 1
  25. 2
  26. 3
  27. 5
  28. 7872
  29. 5797
  30. 8
  31. 7678
  32. 5604
  33. 1701
  34. 4
  35. 2
  36. 4
  37. 2
  38. 12
  39. 6
  40. 2

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