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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 123 · 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.What is the smallest number you must add to 715 so that it divides exactly by 9?
  2. 2.What is the smallest number you must take away from 214 so that it divides exactly by 6?
  3. 3.Which of these numbers divides exactly by 3? (a) 3007 (b) 7159 (c) 1883 (d) 6333
  4. 4.How many factors does 94 have?
  5. 5.What is the smallest number you must add to 207 so that it divides exactly by 7?
  6. 6.Which of these numbers divides exactly by 3? (a) 5687 (b) 5505 (c) 4535 (d) 2203
  7. 7.Which of these numbers divides exactly by 3? (a) 2516 (b) 2388 (c) 7169 (d) 4312
  8. 8.What is the smallest number you must take away from 316 so that it divides exactly by 8?
  9. 9.How many factors does 86 have?
  10. 10.Which of these numbers divides exactly by 9? (a) 6836 (b) 9682 (c) 5865 (d) 2871
  11. 11.What is the smallest number you must add to 888 so that it divides exactly by 7?
  12. 12.How many factors does 32 have?
  13. 13.What is the smallest number you must add to 933 so that it divides exactly by 8?
  14. 14.How many factors does 41 have?
  15. 15.What is the smallest number you must add to 218 so that it divides exactly by 3?
  16. 16.What is the smallest number you must add to 599 so that it divides exactly by 12?
  17. 17.How many factors does 22 have?
  18. 18.What is the smallest number you must take away from 875 so that it divides exactly by 9?
  19. 19.How many factors does 23 have?
  20. 20.How many factors does 70 have?
  21. 21.How many factors does 66 have?
  22. 22.What is the smallest number you must add to 907 so that it divides exactly by 8?
  23. 23.What is the smallest number you must add to 353 so that it divides exactly by 13?
  24. 24.Which of these numbers divides exactly by 4? (a) 3750 (b) 8763 (c) 5604 (d) 4405
  25. 25.How many factors does 37 have?
  26. 26.How many factors does 73 have?
  27. 27.What is the smallest number you must add to 750 so that it divides exactly by 8?
  28. 28.How many factors does 20 have?
  29. 29.What is the smallest number you must add to 634 so that it divides exactly by 3?
  30. 30.What is the smallest number you must take away from 426 so that it divides exactly by 7?
  31. 31.What is the smallest number you must take away from 314 so that it divides exactly by 3?
  32. 32.What is the smallest number you must add to 476 so that it divides exactly by 6?
  33. 33.What is the smallest number you must add to 496 so that it divides exactly by 7?
  34. 34.Which of these numbers divides exactly by 8? (a) 9694 (b) 1698 (c) 1663 (d) 2784
  35. 35.What is the smallest number you must add to 841 so that it divides exactly by 4?
  36. 36.What is the smallest number you must take away from 694 so that it divides exactly by 9?
  37. 37.Which of these numbers divides exactly by 11? (a) 2132 (b) 9537 (c) 7768 (d) 3251
  38. 38.What is the smallest number you must add to 249 so that it divides exactly by 7?
  39. 39.What is the smallest number you must take away from 993 so that it divides exactly by 12?
  40. 40.How many factors does 81 have?

Answer key

  1. 5
  2. 4
  3. 6333
  4. 4
  5. 3
  6. 5505
  7. 2388
  8. 4
  9. 4
  10. 2871
  11. 1
  12. 6
  13. 3
  14. 2
  15. 1
  16. 1
  17. 4
  18. 2
  19. 2
  20. 8
  21. 8
  22. 5
  23. 11
  24. 5604
  25. 2
  26. 2
  27. 2
  28. 6
  29. 2
  30. 6
  31. 2
  32. 4
  33. 1
  34. 2784
  35. 3
  36. 1
  37. 9537
  38. 3
  39. 9
  40. 5

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