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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 193 · 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 23 have?
  2. 2.What is the smallest number you must take away from 239 so that it divides exactly by 8?
  3. 3.Which of these numbers divides exactly by 6? (a) 8123 (b) 9117 (c) 3219 (d) 9396
  4. 4.What is the smallest number you must add to 659 so that it divides exactly by 7?
  5. 5.What is the smallest number you must take away from 684 so that it divides exactly by 7?
  6. 6.What is the smallest number you must add to 291 so that it divides exactly by 11?
  7. 7.How many factors does 30 have?
  8. 8.How many factors does 72 have?
  9. 9.What is the smallest number you must take away from 266 so that it divides exactly by 3?
  10. 10.What is the smallest number you must take away from 299 so that it divides exactly by 7?
  11. 11.What is the smallest number you must take away from 104 so that it divides exactly by 11?
  12. 12.Which of these numbers divides exactly by 11? (a) 3137 (b) 1886 (c) 4675 (d) 9706
  13. 13.What is the smallest number you must take away from 313 so that it divides exactly by 3?
  14. 14.Which of these numbers divides exactly by 4? (a) 7444 (b) 7735 (c) 5535 (d) 2898
  15. 15.What is the smallest number you must add to 935 so that it divides exactly by 7?
  16. 16.How many factors does 73 have?
  17. 17.What is the smallest number you must take away from 629 so that it divides exactly by 13?
  18. 18.What is the smallest number you must take away from 457 so that it divides exactly by 6?
  19. 19.How many factors does 77 have?
  20. 20.Which of these numbers divides exactly by 9? (a) 7785 (b) 2669 (c) 2626 (d) 4760
  21. 21.How many factors does 43 have?
  22. 22.How many factors does 97 have?
  23. 23.What is the smallest number you must add to 127 so that it divides exactly by 9?
  24. 24.What is the smallest number you must add to 428 so that it divides exactly by 8?
  25. 25.What is the smallest number you must take away from 660 so that it divides exactly by 8?
  26. 26.What is the smallest number you must add to 563 so that it divides exactly by 3?
  27. 27.Which of these numbers divides exactly by 11? (a) 7918 (b) 4262 (c) 1782 (d) 5623
  28. 28.How many factors does 17 have?
  29. 29.What is the smallest number you must take away from 292 so that it divides exactly by 3?
  30. 30.What is the smallest number you must add to 707 so that it divides exactly by 4?
  31. 31.How many factors does 96 have?
  32. 32.Which of these numbers divides exactly by 8? (a) 7958 (b) 8907 (c) 1728 (d) 9495
  33. 33.How many factors does 74 have?
  34. 34.Which of these numbers divides exactly by 9? (a) 7555 (b) 2352 (c) 4806 (d) 6024
  35. 35.How many factors does 38 have?
  36. 36.How many factors does 71 have?
  37. 37.Which of these numbers divides exactly by 3? (a) 4030 (b) 3620 (c) 6075 (d) 3356
  38. 38.How many factors does 90 have?
  39. 39.What is the smallest number you must take away from 997 so that it divides exactly by 11?
  40. 40.What is the smallest number you must take away from 168 so that it divides exactly by 13?

Answer key

  1. 2
  2. 7
  3. 9396
  4. 6
  5. 5
  6. 6
  7. 8
  8. 12
  9. 2
  10. 5
  11. 5
  12. 4675
  13. 1
  14. 7444
  15. 3
  16. 2
  17. 5
  18. 1
  19. 4
  20. 7785
  21. 2
  22. 2
  23. 8
  24. 4
  25. 4
  26. 1
  27. 1782
  28. 2
  29. 1
  30. 1
  31. 12
  32. 1728
  33. 4
  34. 4806
  35. 4
  36. 2
  37. 6075
  38. 12
  39. 7
  40. 12

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