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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 172 · 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.How many factors does 35 have?
  2. 2.Which of these numbers divides exactly by 6? (a) 9853 (b) 3868 (c) 1714 (d) 3906
  3. 3.Which of these numbers divides exactly by 8? (a) 4540 (b) 2649 (c) 1059 (d) 5920
  4. 4.How many factors does 40 have?
  5. 5.How many factors does 73 have?
  6. 6.How many factors does 64 have?
  7. 7.Which of these numbers divides exactly by 6? (a) 6913 (b) 2882 (c) 6038 (d) 3522
  8. 8.How many factors does 57 have?
  9. 9.What is the smallest number you must take away from 333 so that it divides exactly by 4?
  10. 10.What is the smallest number you must add to 239 so that it divides exactly by 9?
  11. 11.What is the smallest number you must take away from 727 so that it divides exactly by 8?
  12. 12.Which of these numbers divides exactly by 3? (a) 9835 (b) 3616 (c) 7573 (d) 1929
  13. 13.Which of these numbers divides exactly by 4? (a) 4217 (b) 9424 (c) 5525 (d) 2629
  14. 14.What is the smallest number you must add to 765 so that it divides exactly by 12?
  15. 15.What is the smallest number you must take away from 950 so that it divides exactly by 6?
  16. 16.How many factors does 43 have?
  17. 17.How many factors does 70 have?
  18. 18.How many factors does 91 have?
  19. 19.Which of these numbers divides exactly by 4? (a) 6783 (b) 3896 (c) 8686 (d) 9985
  20. 20.How many factors does 16 have?
  21. 21.How many factors does 85 have?
  22. 22.How many factors does 53 have?
  23. 23.What is the smallest number you must add to 783 so that it divides exactly by 12?
  24. 24.How many factors does 96 have?
  25. 25.Which of these numbers divides exactly by 8? (a) 4486 (b) 3852 (c) 2182 (d) 1680
  26. 26.What is the smallest number you must add to 367 so that it divides exactly by 9?
  27. 27.What is the smallest number you must take away from 110 so that it divides exactly by 4?
  28. 28.Which of these numbers divides exactly by 11? (a) 5771 (b) 6166 (c) 2101 (d) 5612
  29. 29.What is the smallest number you must add to 904 so that it divides exactly by 12?
  30. 30.What is the smallest number you must add to 116 so that it divides exactly by 8?
  31. 31.What is the smallest number you must take away from 284 so that it divides exactly by 3?
  32. 32.How many factors does 29 have?
  33. 33.What is the smallest number you must take away from 750 so that it divides exactly by 9?
  34. 34.How many factors does 66 have?
  35. 35.Which of these numbers divides exactly by 9? (a) 3543 (b) 6362 (c) 6444 (d) 2409
  36. 36.How many factors does 34 have?
  37. 37.Which of these numbers divides exactly by 11? (a) 1567 (b) 3866 (c) 2373 (d) 5379
  38. 38.How many factors does 79 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 2066 (b) 5887 (c) 3189 (d) 5876
  40. 40.What is the smallest number you must take away from 943 so that it divides exactly by 13?

Answer key

  1. 4
  2. 3906
  3. 5920
  4. 8
  5. 2
  6. 7
  7. 3522
  8. 4
  9. 1
  10. 4
  11. 7
  12. 1929
  13. 9424
  14. 3
  15. 2
  16. 2
  17. 8
  18. 4
  19. 3896
  20. 5
  21. 4
  22. 2
  23. 9
  24. 12
  25. 1680
  26. 2
  27. 2
  28. 2101
  29. 8
  30. 4
  31. 2
  32. 2
  33. 3
  34. 8
  35. 6444
  36. 4
  37. 5379
  38. 2
  39. 3189
  40. 7

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