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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 169 · 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 84 have?
  2. 2.How many factors does 51 have?
  3. 3.What is the smallest number you must take away from 504 so that it divides exactly by 11?
  4. 4.How many factors does 47 have?
  5. 5.How many factors does 86 have?
  6. 6.How many factors does 52 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 2096 (b) 9185 (c) 6876 (d) 4534
  8. 8.What is the smallest number you must add to 539 so that it divides exactly by 12?
  9. 9.What is the smallest number you must take away from 779 so that it divides exactly by 7?
  10. 10.What is the smallest number you must add to 201 so that it divides exactly by 4?
  11. 11.What is the smallest number you must add to 463 so that it divides exactly by 7?
  12. 12.Which of these numbers divides exactly by 9? (a) 6622 (b) 9327 (c) 6930 (d) 2716
  13. 13.Which of these numbers divides exactly by 4? (a) 6601 (b) 1906 (c) 7054 (d) 9160
  14. 14.What is the smallest number you must add to 593 so that it divides exactly by 12?
  15. 15.Which of these numbers divides exactly by 9? (a) 9093 (b) 1131 (c) 3015 (d) 7554
  16. 16.How many factors does 21 have?
  17. 17.What is the smallest number you must add to 474 so that it divides exactly by 13?
  18. 18.What is the smallest number you must take away from 106 so that it divides exactly by 9?
  19. 19.How many factors does 60 have?
  20. 20.What is the smallest number you must take away from 781 so that it divides exactly by 13?
  21. 21.Which of these numbers divides exactly by 4? (a) 5067 (b) 8345 (c) 3129 (d) 7664
  22. 22.Which of these numbers divides exactly by 3? (a) 6506 (b) 8197 (c) 4503 (d) 4246
  23. 23.What is the smallest number you must add to 225 so that it divides exactly by 6?
  24. 24.What is the smallest number you must add to 782 so that it divides exactly by 9?
  25. 25.How many factors does 75 have?
  26. 26.What is the smallest number you must add to 204 so that it divides exactly by 8?
  27. 27.How many factors does 31 have?
  28. 28.What is the smallest number you must take away from 317 so that it divides exactly by 9?
  29. 29.Which of these numbers divides exactly by 11? (a) 9955 (b) 6272 (c) 3184 (d) 5747
  30. 30.How many factors does 56 have?
  31. 31.What is the smallest number you must take away from 355 so that it divides exactly by 7?
  32. 32.What is the smallest number you must add to 550 so that it divides exactly by 6?
  33. 33.How many factors does 41 have?
  34. 34.How many factors does 70 have?
  35. 35.Which of these numbers divides exactly by 3? (a) 6157 (b) 5961 (c) 4972 (d) 8323
  36. 36.What is the smallest number you must add to 341 so that it divides exactly by 6?
  37. 37.How many factors does 16 have?
  38. 38.How many factors does 33 have?
  39. 39.Which of these numbers divides exactly by 9? (a) 4747 (b) 1809 (c) 3498 (d) 2454
  40. 40.What is the smallest number you must take away from 716 so that it divides exactly by 6?

Answer key

  1. 12
  2. 4
  3. 9
  4. 2
  5. 4
  6. 6
  7. 9185
  8. 1
  9. 2
  10. 3
  11. 6
  12. 6930
  13. 9160
  14. 7
  15. 3015
  16. 4
  17. 7
  18. 7
  19. 12
  20. 1
  21. 7664
  22. 4503
  23. 3
  24. 1
  25. 6
  26. 4
  27. 2
  28. 2
  29. 9955
  30. 8
  31. 5
  32. 2
  33. 2
  34. 8
  35. 5961
  36. 1
  37. 5
  38. 4
  39. 1809
  40. 2

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