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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 70 · 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 129 so that it divides exactly by 4?
  2. 2.What is the smallest number you must add to 643 so that it divides exactly by 7?
  3. 3.What is the smallest number you must add to 915 so that it divides exactly by 8?
  4. 4.Which of these numbers divides exactly by 8? (a) 7619 (b) 1004 (c) 1702 (d) 7544
  5. 5.How many factors does 29 have?
  6. 6.What is the smallest number you must take away from 842 so that it divides exactly by 13?
  7. 7.What is the smallest number you must take away from 211 so that it divides exactly by 4?
  8. 8.What is the smallest number you must take away from 224 so that it divides exactly by 9?
  9. 9.How many factors does 27 have?
  10. 10.How many factors does 65 have?
  11. 11.What is the smallest number you must add to 722 so that it divides exactly by 11?
  12. 12.Which of these numbers divides exactly by 8? (a) 4618 (b) 5833 (c) 7518 (d) 4984
  13. 13.How many factors does 68 have?
  14. 14.What is the smallest number you must add to 634 so that it divides exactly by 12?
  15. 15.Which of these numbers divides exactly by 3? (a) 5075 (b) 2953 (c) 3252 (d) 2557
  16. 16.How many factors does 36 have?
  17. 17.Which of these numbers divides exactly by 6? (a) 9540 (b) 9071 (c) 7100 (d) 2782
  18. 18.How many factors does 78 have?
  19. 19.How many factors does 86 have?
  20. 20.What is the smallest number you must take away from 237 so that it divides exactly by 13?
  21. 21.How many factors does 92 have?
  22. 22.Which of these numbers divides exactly by 8? (a) 9784 (b) 8577 (c) 4379 (d) 6141
  23. 23.What is the smallest number you must add to 902 so that it divides exactly by 13?
  24. 24.What is the smallest number you must add to 512 so that it divides exactly by 3?
  25. 25.Which of these numbers divides exactly by 6? (a) 3184 (b) 7524 (c) 3370 (d) 8506
  26. 26.Which of these numbers divides exactly by 9? (a) 4388 (b) 5076 (c) 2147 (d) 7106
  27. 27.What is the smallest number you must take away from 592 so that it divides exactly by 12?
  28. 28.How many factors does 69 have?
  29. 29.Which of these numbers divides exactly by 3? (a) 8958 (b) 2573 (c) 7141 (d) 7502
  30. 30.What is the smallest number you must add to 724 so that it divides exactly by 3?
  31. 31.How many factors does 37 have?
  32. 32.How many factors does 61 have?
  33. 33.How many factors does 52 have?
  34. 34.How many factors does 23 have?
  35. 35.How many factors does 40 have?
  36. 36.What is the smallest number you must add to 362 so that it divides exactly by 13?
  37. 37.Which of these numbers divides exactly by 9? (a) 6640 (b) 5089 (c) 9522 (d) 2413
  38. 38.How many factors does 70 have?
  39. 39.What is the smallest number you must add to 254 so that it divides exactly by 13?
  40. 40.Which of these numbers divides exactly by 8? (a) 8570 (b) 4208 (c) 7182 (d) 8699

Answer key

  1. 3
  2. 1
  3. 5
  4. 7544
  5. 2
  6. 10
  7. 3
  8. 8
  9. 4
  10. 4
  11. 4
  12. 4984
  13. 6
  14. 2
  15. 3252
  16. 9
  17. 9540
  18. 8
  19. 4
  20. 3
  21. 6
  22. 9784
  23. 8
  24. 1
  25. 7524
  26. 5076
  27. 4
  28. 4
  29. 8958
  30. 2
  31. 2
  32. 2
  33. 6
  34. 2
  35. 8
  36. 2
  37. 9522
  38. 8
  39. 6
  40. 4208

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