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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 196 · 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 74 have?
  2. 2.How many factors does 33 have?
  3. 3.How many factors does 32 have?
  4. 4.Which of these numbers divides exactly by 3? (a) 6742 (b) 2552 (c) 2378 (d) 7641
  5. 5.What is the smallest number you must add to 286 so that it divides exactly by 3?
  6. 6.How many factors does 18 have?
  7. 7.Which of these numbers divides exactly by 4? (a) 2698 (b) 5161 (c) 8812 (d) 3597
  8. 8.How many factors does 67 have?
  9. 9.How many factors does 31 have?
  10. 10.What is the smallest number you must add to 921 so that it divides exactly by 11?
  11. 11.What is the smallest number you must add to 304 so that it divides exactly by 7?
  12. 12.How many factors does 94 have?
  13. 13.Which of these numbers divides exactly by 8? (a) 7912 (b) 9132 (c) 7287 (d) 9807
  14. 14.What is the smallest number you must take away from 755 so that it divides exactly by 11?
  15. 15.Which of these numbers divides exactly by 8? (a) 1919 (b) 7753 (c) 7448 (d) 8595
  16. 16.Which of these numbers divides exactly by 6? (a) 6133 (b) 6134 (c) 4355 (d) 8934
  17. 17.How many factors does 55 have?
  18. 18.How many factors does 85 have?
  19. 19.What is the smallest number you must add to 355 so that it divides exactly by 4?
  20. 20.What is the smallest number you must add to 961 so that it divides exactly by 11?
  21. 21.How many factors does 14 have?
  22. 22.How many factors does 40 have?
  23. 23.What is the smallest number you must take away from 329 so that it divides exactly by 13?
  24. 24.What is the smallest number you must take away from 106 so that it divides exactly by 4?
  25. 25.How many factors does 29 have?
  26. 26.What is the smallest number you must take away from 943 so that it divides exactly by 6?
  27. 27.Which of these numbers divides exactly by 6? (a) 3659 (b) 7251 (c) 8535 (d) 3306
  28. 28.Which of these numbers divides exactly by 6? (a) 6898 (b) 3920 (c) 8483 (d) 1980
  29. 29.What is the smallest number you must add to 515 so that it divides exactly by 4?
  30. 30.How many factors does 35 have?
  31. 31.Which of these numbers divides exactly by 4? (a) 5647 (b) 2356 (c) 2867 (d) 7931
  32. 32.Which of these numbers divides exactly by 8? (a) 3996 (b) 2998 (c) 9956 (d) 4008
  33. 33.How many factors does 91 have?
  34. 34.What is the smallest number you must take away from 892 so that it divides exactly by 7?
  35. 35.What is the smallest number you must add to 707 so that it divides exactly by 9?
  36. 36.Which of these numbers divides exactly by 4? (a) 4854 (b) 8866 (c) 4286 (d) 3864
  37. 37.What is the smallest number you must take away from 241 so that it divides exactly by 7?
  38. 38.What is the smallest number you must add to 566 so that it divides exactly by 7?
  39. 39.What is the smallest number you must take away from 785 so that it divides exactly by 11?
  40. 40.What is the smallest number you must add to 154 so that it divides exactly by 9?

Answer key

  1. 4
  2. 4
  3. 6
  4. 7641
  5. 2
  6. 6
  7. 8812
  8. 2
  9. 2
  10. 3
  11. 4
  12. 4
  13. 7912
  14. 7
  15. 7448
  16. 8934
  17. 4
  18. 4
  19. 1
  20. 7
  21. 4
  22. 8
  23. 4
  24. 2
  25. 2
  26. 1
  27. 3306
  28. 1980
  29. 1
  30. 4
  31. 2356
  32. 4008
  33. 4
  34. 3
  35. 4
  36. 3864
  37. 3
  38. 1
  39. 4
  40. 8

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