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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 154 · 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 11? (a) 3225 (b) 7264 (c) 2702 (d) 6864
  2. 2.How many factors does 20 have?
  3. 3.What is the smallest number you must take away from 669 so that it divides exactly by 11?
  4. 4.What is the smallest number you must take away from 486 so that it divides exactly by 11?
  5. 5.What is the smallest number you must take away from 820 so that it divides exactly by 11?
  6. 6.How many factors does 39 have?
  7. 7.What is the smallest number you must take away from 748 so that it divides exactly by 7?
  8. 8.How many factors does 78 have?
  9. 9.What is the smallest number you must add to 426 so that it divides exactly by 11?
  10. 10.How many factors does 84 have?
  11. 11.What is the smallest number you must take away from 555 so that it divides exactly by 6?
  12. 12.Which of these numbers divides exactly by 4? (a) 7256 (b) 1987 (c) 1878 (d) 9102
  13. 13.How many factors does 36 have?
  14. 14.What is the smallest number you must add to 233 so that it divides exactly by 11?
  15. 15.Which of these numbers divides exactly by 6? (a) 8791 (b) 8026 (c) 4050 (d) 3124
  16. 16.What is the smallest number you must take away from 207 so that it divides exactly by 13?
  17. 17.How many factors does 51 have?
  18. 18.What is the smallest number you must take away from 637 so that it divides exactly by 6?
  19. 19.What is the smallest number you must take away from 815 so that it divides exactly by 13?
  20. 20.How many factors does 55 have?
  21. 21.How many factors does 98 have?
  22. 22.What is the smallest number you must add to 898 so that it divides exactly by 12?
  23. 23.How many factors does 75 have?
  24. 24.What is the smallest number you must add to 567 so that it divides exactly by 12?
  25. 25.What is the smallest number you must add to 229 so that it divides exactly by 12?
  26. 26.How many factors does 35 have?
  27. 27.What is the smallest number you must take away from 827 so that it divides exactly by 3?
  28. 28.What is the smallest number you must take away from 233 so that it divides exactly by 12?
  29. 29.Which of these numbers divides exactly by 6? (a) 4111 (b) 2327 (c) 2199 (d) 6072
  30. 30.What is the smallest number you must take away from 103 so that it divides exactly by 3?
  31. 31.Which of these numbers divides exactly by 9? (a) 8325 (b) 4623 (c) 7876 (d) 3524
  32. 32.What is the smallest number you must add to 802 so that it divides exactly by 12?
  33. 33.What is the smallest number you must add to 160 so that it divides exactly by 13?
  34. 34.Which of these numbers divides exactly by 6? (a) 2014 (b) 4866 (c) 2563 (d) 2193
  35. 35.Which of these numbers divides exactly by 9? (a) 9508 (b) 9802 (c) 1161 (d) 6323
  36. 36.Which of these numbers divides exactly by 9? (a) 4221 (b) 1298 (c) 3613 (d) 8176
  37. 37.How many factors does 49 have?
  38. 38.What is the smallest number you must add to 579 so that it divides exactly by 13?
  39. 39.Which of these numbers divides exactly by 6? (a) 7416 (b) 8098 (c) 4496 (d) 4346
  40. 40.How many factors does 57 have?

Answer key

  1. 6864
  2. 6
  3. 9
  4. 2
  5. 6
  6. 4
  7. 6
  8. 8
  9. 3
  10. 12
  11. 3
  12. 7256
  13. 9
  14. 9
  15. 4050
  16. 12
  17. 4
  18. 1
  19. 9
  20. 4
  21. 6
  22. 2
  23. 6
  24. 9
  25. 11
  26. 4
  27. 2
  28. 5
  29. 6072
  30. 1
  31. 8325
  32. 2
  33. 9
  34. 4866
  35. 1161
  36. 4221
  37. 3
  38. 6
  39. 7416
  40. 4

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