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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 133 · 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 205 so that it divides exactly by 12?
  2. 2.How many factors does 64 have?
  3. 3.How many factors does 77 have?
  4. 4.Which of these numbers divides exactly by 3? (a) 6875 (b) 3780 (c) 3196 (d) 2156
  5. 5.How many factors does 95 have?
  6. 6.What is the smallest number you must add to 797 so that it divides exactly by 9?
  7. 7.How many factors does 79 have?
  8. 8.How many factors does 91 have?
  9. 9.Which of these numbers divides exactly by 4? (a) 5262 (b) 3022 (c) 4048 (d) 1402
  10. 10.Which of these numbers divides exactly by 6? (a) 9424 (b) 8803 (c) 1680 (d) 5309
  11. 11.Which of these numbers divides exactly by 6? (a) 7770 (b) 3921 (c) 7946 (d) 2738
  12. 12.How many factors does 60 have?
  13. 13.Which of these numbers divides exactly by 3? (a) 3209 (b) 7513 (c) 2928 (d) 1381
  14. 14.What is the smallest number you must take away from 680 so that it divides exactly by 7?
  15. 15.How many factors does 86 have?
  16. 16.How many factors does 66 have?
  17. 17.Which of these numbers divides exactly by 9? (a) 3639 (b) 8172 (c) 6236 (d) 5757
  18. 18.What is the smallest number you must add to 629 so that it divides exactly by 12?
  19. 19.How many factors does 53 have?
  20. 20.How many factors does 31 have?
  21. 21.How many factors does 34 have?
  22. 22.What is the smallest number you must add to 200 so that it divides exactly by 13?
  23. 23.Which of these numbers divides exactly by 9? (a) 3953 (b) 5282 (c) 2438 (d) 2484
  24. 24.How many factors does 37 have?
  25. 25.Which of these numbers divides exactly by 9? (a) 7509 (b) 3591 (c) 2786 (d) 7052
  26. 26.What is the smallest number you must add to 128 so that it divides exactly by 13?
  27. 27.What is the smallest number you must add to 855 so that it divides exactly by 13?
  28. 28.What is the smallest number you must take away from 964 so that it divides exactly by 12?
  29. 29.What is the smallest number you must add to 202 so that it divides exactly by 13?
  30. 30.How many factors does 33 have?
  31. 31.What is the smallest number you must add to 950 so that it divides exactly by 3?
  32. 32.How many factors does 25 have?
  33. 33.Which of these numbers divides exactly by 9? (a) 2554 (b) 2025 (c) 2856 (d) 7955
  34. 34.Which of these numbers divides exactly by 6? (a) 6576 (b) 2605 (c) 3483 (d) 3080
  35. 35.What is the smallest number you must add to 319 so that it divides exactly by 6?
  36. 36.Which of these numbers divides exactly by 8? (a) 2922 (b) 2084 (c) 1677 (d) 7168
  37. 37.How many factors does 51 have?
  38. 38.Which of these numbers divides exactly by 6? (a) 8066 (b) 2472 (c) 1913 (d) 9187
  39. 39.Which of these numbers divides exactly by 6? (a) 3262 (b) 5869 (c) 2035 (d) 4008
  40. 40.What is the smallest number you must add to 421 so that it divides exactly by 13?

Answer key

  1. 11
  2. 7
  3. 4
  4. 3780
  5. 4
  6. 4
  7. 2
  8. 4
  9. 4048
  10. 1680
  11. 7770
  12. 12
  13. 2928
  14. 1
  15. 4
  16. 8
  17. 8172
  18. 7
  19. 2
  20. 2
  21. 4
  22. 8
  23. 2484
  24. 2
  25. 3591
  26. 2
  27. 3
  28. 4
  29. 6
  30. 4
  31. 1
  32. 3
  33. 2025
  34. 6576
  35. 5
  36. 7168
  37. 4
  38. 2472
  39. 4008
  40. 8

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