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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 322 · 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 83 have?
  2. 2.What is the smallest number you must take away from 221 so that it divides exactly by 11?
  3. 3.How many factors does 54 have?
  4. 4.What is the smallest number you must add to 450 so that it divides exactly by 13?
  5. 5.Which of these numbers divides exactly by 8? (a) 6784 (b) 3387 (c) 2369 (d) 1871
  6. 6.What is the smallest number you must take away from 749 so that it divides exactly by 11?
  7. 7.What is the smallest number you must add to 275 so that it divides exactly by 9?
  8. 8.What is the smallest number you must take away from 549 so that it divides exactly by 8?
  9. 9.How many factors does 65 have?
  10. 10.How many factors does 27 have?
  11. 11.Which of these numbers divides exactly by 9? (a) 8892 (b) 4233 (c) 8274 (d) 9365
  12. 12.How many factors does 52 have?
  13. 13.What is the smallest number you must add to 590 so that it divides exactly by 7?
  14. 14.What is the smallest number you must add to 263 so that it divides exactly by 12?
  15. 15.Which of these numbers divides exactly by 8? (a) 7565 (b) 6799 (c) 4069 (d) 7944
  16. 16.How many factors does 75 have?
  17. 17.Which of these numbers divides exactly by 8? (a) 9283 (b) 9312 (c) 9639 (d) 2852
  18. 18.Which of these numbers divides exactly by 9? (a) 4707 (b) 1225 (c) 7370 (d) 2398
  19. 19.Which of these numbers divides exactly by 4? (a) 9715 (b) 4704 (c) 5125 (d) 6667
  20. 20.Which of these numbers divides exactly by 9? (a) 3038 (b) 7901 (c) 9895 (d) 4320
  21. 21.What is the smallest number you must add to 286 so that it divides exactly by 4?
  22. 22.Which of these numbers divides exactly by 11? (a) 4521 (b) 3920 (c) 6508 (d) 1817
  23. 23.How many factors does 47 have?
  24. 24.Which of these numbers divides exactly by 6? (a) 1068 (b) 2716 (c) 1168 (d) 3517
  25. 25.How many factors does 70 have?
  26. 26.Which of these numbers divides exactly by 8? (a) 7395 (b) 1784 (c) 2669 (d) 1549
  27. 27.What is the smallest number you must take away from 692 so that it divides exactly by 8?
  28. 28.How many factors does 90 have?
  29. 29.What is the smallest number you must add to 690 so that it divides exactly by 12?
  30. 30.How many factors does 41 have?
  31. 31.What is the smallest number you must add to 574 so that it divides exactly by 13?
  32. 32.What is the smallest number you must take away from 758 so that it divides exactly by 6?
  33. 33.Which of these numbers divides exactly by 3? (a) 6649 (b) 9084 (c) 1520 (d) 3674
  34. 34.Which of these numbers divides exactly by 3? (a) 3773 (b) 4016 (c) 4986 (d) 9067
  35. 35.What is the smallest number you must add to 249 so that it divides exactly by 4?
  36. 36.What is the smallest number you must add to 751 so that it divides exactly by 11?
  37. 37.How many factors does 33 have?
  38. 38.How many factors does 89 have?
  39. 39.Which of these numbers divides exactly by 8? (a) 9928 (b) 6575 (c) 4618 (d) 8262
  40. 40.How many factors does 97 have?

Answer key

  1. 2
  2. 1
  3. 8
  4. 5
  5. 6784
  6. 1
  7. 4
  8. 5
  9. 4
  10. 4
  11. 8892
  12. 6
  13. 5
  14. 1
  15. 7944
  16. 6
  17. 9312
  18. 4707
  19. 4704
  20. 4320
  21. 2
  22. 4521
  23. 2
  24. 1068
  25. 8
  26. 1784
  27. 4
  28. 12
  29. 6
  30. 2
  31. 11
  32. 2
  33. 9084
  34. 4986
  35. 3
  36. 8
  37. 4
  38. 2
  39. 9928
  40. 2

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