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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 235 · 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 922 so that it divides exactly by 9?
  2. 2.How many factors does 65 have?
  3. 3.What is the smallest number you must add to 268 so that it divides exactly by 3?
  4. 4.Which of these numbers divides exactly by 11? (a) 6137 (b) 9668 (c) 5995 (d) 2947
  5. 5.What is the smallest number you must add to 721 so that it divides exactly by 8?
  6. 6.How many factors does 19 have?
  7. 7.What is the smallest number you must take away from 767 so that it divides exactly by 6?
  8. 8.Which of these numbers divides exactly by 8? (a) 2630 (b) 1224 (c) 6121 (d) 1822
  9. 9.How many factors does 40 have?
  10. 10.What is the smallest number you must take away from 137 so that it divides exactly by 4?
  11. 11.What is the smallest number you must add to 688 so that it divides exactly by 3?
  12. 12.What is the smallest number you must take away from 956 so that it divides exactly by 6?
  13. 13.How many factors does 44 have?
  14. 14.What is the smallest number you must take away from 111 so that it divides exactly by 8?
  15. 15.How many factors does 28 have?
  16. 16.What is the smallest number you must take away from 665 so that it divides exactly by 8?
  17. 17.Which of these numbers divides exactly by 4? (a) 9201 (b) 2491 (c) 3783 (d) 7124
  18. 18.What is the smallest number you must add to 326 so that it divides exactly by 11?
  19. 19.How many factors does 83 have?
  20. 20.How many factors does 91 have?
  21. 21.How many factors does 27 have?
  22. 22.How many factors does 66 have?
  23. 23.What is the smallest number you must add to 469 so that it divides exactly by 3?
  24. 24.Which of these numbers divides exactly by 8? (a) 4144 (b) 3706 (c) 3404 (d) 2806
  25. 25.How many factors does 96 have?
  26. 26.What is the smallest number you must take away from 683 so that it divides exactly by 11?
  27. 27.What is the smallest number you must take away from 742 so that it divides exactly by 11?
  28. 28.How many factors does 13 have?
  29. 29.Which of these numbers divides exactly by 3? (a) 7013 (b) 9313 (c) 1189 (d) 6396
  30. 30.What is the smallest number you must take away from 587 so that it divides exactly by 6?
  31. 31.What is the smallest number you must add to 814 so that it divides exactly by 13?
  32. 32.What is the smallest number you must take away from 750 so that it divides exactly by 7?
  33. 33.How many factors does 92 have?
  34. 34.How many factors does 24 have?
  35. 35.How many factors does 70 have?
  36. 36.What is the smallest number you must add to 906 so that it divides exactly by 12?
  37. 37.Which of these numbers divides exactly by 6? (a) 9176 (b) 2274 (c) 4586 (d) 5656
  38. 38.What is the smallest number you must take away from 740 so that it divides exactly by 6?
  39. 39.Which of these numbers divides exactly by 6? (a) 8875 (b) 3783 (c) 1824 (d) 6753
  40. 40.How many factors does 16 have?

Answer key

  1. 5
  2. 4
  3. 2
  4. 5995
  5. 7
  6. 2
  7. 5
  8. 1224
  9. 8
  10. 1
  11. 2
  12. 2
  13. 6
  14. 7
  15. 6
  16. 1
  17. 7124
  18. 4
  19. 2
  20. 4
  21. 4
  22. 8
  23. 2
  24. 4144
  25. 12
  26. 1
  27. 5
  28. 2
  29. 6396
  30. 5
  31. 5
  32. 1
  33. 6
  34. 8
  35. 8
  36. 6
  37. 2274
  38. 2
  39. 1824
  40. 5

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