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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 8 · 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 39 have?
  2. 2.How many factors does 35 have?
  3. 3.What is the smallest number you must add to 885 so that it divides exactly by 4?
  4. 4.How many factors does 58 have?
  5. 5.How many factors does 18 have?
  6. 6.What is the smallest number you must add to 879 so that it divides exactly by 8?
  7. 7.Which of these numbers divides exactly by 6? (a) 2897 (b) 1920 (c) 4461 (d) 9416
  8. 8.How many factors does 23 have?
  9. 9.What is the smallest number you must add to 233 so that it divides exactly by 11?
  10. 10.How many factors does 15 have?
  11. 11.How many factors does 50 have?
  12. 12.How many factors does 70 have?
  13. 13.What is the smallest number you must add to 461 so that it divides exactly by 12?
  14. 14.What is the smallest number you must add to 484 so that it divides exactly by 9?
  15. 15.How many factors does 56 have?
  16. 16.What is the smallest number you must take away from 933 so that it divides exactly by 8?
  17. 17.What is the smallest number you must take away from 740 so that it divides exactly by 8?
  18. 18.How many factors does 62 have?
  19. 19.What is the smallest number you must take away from 654 so that it divides exactly by 13?
  20. 20.How many factors does 46 have?
  21. 21.What is the smallest number you must take away from 346 so that it divides exactly by 7?
  22. 22.What is the smallest number you must take away from 753 so that it divides exactly by 4?
  23. 23.What is the smallest number you must add to 298 so that it divides exactly by 7?
  24. 24.What is the smallest number you must add to 183 so that it divides exactly by 11?
  25. 25.Which of these numbers divides exactly by 8? (a) 8264 (b) 1377 (c) 4009 (d) 2289
  26. 26.What is the smallest number you must add to 645 so that it divides exactly by 6?
  27. 27.What is the smallest number you must take away from 676 so that it divides exactly by 7?
  28. 28.What is the smallest number you must take away from 694 so that it divides exactly by 13?
  29. 29.Which of these numbers divides exactly by 4? (a) 1107 (b) 2668 (c) 1826 (d) 5811
  30. 30.How many factors does 95 have?
  31. 31.What is the smallest number you must take away from 978 so that it divides exactly by 11?
  32. 32.What is the smallest number you must add to 130 so that it divides exactly by 4?
  33. 33.What is the smallest number you must take away from 402 so that it divides exactly by 9?
  34. 34.What is the smallest number you must add to 496 so that it divides exactly by 6?
  35. 35.What is the smallest number you must take away from 658 so that it divides exactly by 12?
  36. 36.How many factors does 71 have?
  37. 37.What is the smallest number you must add to 422 so that it divides exactly by 3?
  38. 38.How many factors does 98 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 6457 (b) 2848 (c) 1857 (d) 1478
  40. 40.How many factors does 91 have?

Answer key

  1. 4
  2. 4
  3. 3
  4. 4
  5. 6
  6. 1
  7. 1920
  8. 2
  9. 9
  10. 4
  11. 6
  12. 8
  13. 7
  14. 2
  15. 8
  16. 5
  17. 4
  18. 4
  19. 4
  20. 4
  21. 3
  22. 1
  23. 3
  24. 4
  25. 8264
  26. 3
  27. 4
  28. 5
  29. 2668
  30. 4
  31. 10
  32. 2
  33. 6
  34. 2
  35. 10
  36. 2
  37. 1
  38. 6
  39. 1857
  40. 4

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