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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 263 · 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 take away from 158 so that it divides exactly by 3?
  2. 2.What is the smallest number you must add to 864 so that it divides exactly by 7?
  3. 3.What is the smallest number you must take away from 505 so that it divides exactly by 3?
  4. 4.What is the smallest number you must add to 277 so that it divides exactly by 3?
  5. 5.What is the smallest number you must add to 855 so that it divides exactly by 6?
  6. 6.How many factors does 95 have?
  7. 7.What is the smallest number you must add to 754 so that it divides exactly by 4?
  8. 8.Which of these numbers divides exactly by 4? (a) 8457 (b) 3675 (c) 7960 (d) 5086
  9. 9.What is the smallest number you must add to 340 so that it divides exactly by 13?
  10. 10.How many factors does 70 have?
  11. 11.Which of these numbers divides exactly by 4? (a) 3546 (b) 6177 (c) 9300 (d) 2793
  12. 12.What is the smallest number you must add to 461 so that it divides exactly by 13?
  13. 13.How many factors does 83 have?
  14. 14.What is the smallest number you must add to 703 so that it divides exactly by 12?
  15. 15.How many factors does 26 have?
  16. 16.How many factors does 40 have?
  17. 17.What is the smallest number you must add to 727 so that it divides exactly by 9?
  18. 18.How many factors does 13 have?
  19. 19.How many factors does 29 have?
  20. 20.How many factors does 43 have?
  21. 21.Which of these numbers divides exactly by 6? (a) 7924 (b) 4740 (c) 9976 (d) 9949
  22. 22.How many factors does 82 have?
  23. 23.What is the smallest number you must add to 508 so that it divides exactly by 6?
  24. 24.What is the smallest number you must add to 738 so that it divides exactly by 7?
  25. 25.Which of these numbers divides exactly by 3? (a) 2402 (b) 2022 (c) 2960 (d) 2003
  26. 26.How many factors does 31 have?
  27. 27.What is the smallest number you must take away from 134 so that it divides exactly by 9?
  28. 28.What is the smallest number you must take away from 298 so that it divides exactly by 11?
  29. 29.Which of these numbers divides exactly by 3? (a) 3439 (b) 3100 (c) 5594 (d) 3660
  30. 30.How many factors does 80 have?
  31. 31.Which of these numbers divides exactly by 3? (a) 7676 (b) 6459 (c) 9680 (d) 7295
  32. 32.What is the smallest number you must take away from 224 so that it divides exactly by 9?
  33. 33.What is the smallest number you must take away from 327 so that it divides exactly by 6?
  34. 34.How many factors does 71 have?
  35. 35.What is the smallest number you must add to 423 so that it divides exactly by 4?
  36. 36.What is the smallest number you must take away from 475 so that it divides exactly by 3?
  37. 37.How many factors does 19 have?
  38. 38.How many factors does 72 have?
  39. 39.Which of these numbers divides exactly by 6? (a) 2082 (b) 4845 (c) 6344 (d) 9350
  40. 40.What is the smallest number you must take away from 474 so that it divides exactly by 12?

Answer key

  1. 2
  2. 4
  3. 1
  4. 2
  5. 3
  6. 4
  7. 2
  8. 7960
  9. 11
  10. 8
  11. 9300
  12. 7
  13. 2
  14. 5
  15. 4
  16. 8
  17. 2
  18. 2
  19. 2
  20. 2
  21. 4740
  22. 4
  23. 2
  24. 4
  25. 2022
  26. 2
  27. 8
  28. 1
  29. 3660
  30. 10
  31. 6459
  32. 8
  33. 3
  34. 2
  35. 1
  36. 1
  37. 2
  38. 12
  39. 2082
  40. 6

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