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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 24 · 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.Which of these numbers divides exactly by 8? (a) 2304 (b) 8099 (c) 9073 (d) 6783
  2. 2.What is the smallest number you must add to 776 so that it divides exactly by 7?
  3. 3.How many factors does 86 have?
  4. 4.What is the smallest number you must take away from 926 so that it divides exactly by 9?
  5. 5.What is the smallest number you must take away from 359 so that it divides exactly by 13?
  6. 6.Which of these numbers divides exactly by 3? (a) 5742 (b) 2744 (c) 3275 (d) 3892
  7. 7.What is the smallest number you must take away from 493 so that it divides exactly by 7?
  8. 8.What is the smallest number you must add to 128 so that it divides exactly by 11?
  9. 9.Which of these numbers divides exactly by 11? (a) 4906 (b) 1698 (c) 8471 (d) 2965
  10. 10.What is the smallest number you must add to 529 so that it divides exactly by 4?
  11. 11.How many factors does 67 have?
  12. 12.What is the smallest number you must take away from 699 so that it divides exactly by 4?
  13. 13.How many factors does 19 have?
  14. 14.What is the smallest number you must take away from 787 so that it divides exactly by 4?
  15. 15.How many factors does 74 have?
  16. 16.What is the smallest number you must add to 931 so that it divides exactly by 3?
  17. 17.What is the smallest number you must take away from 187 so that it divides exactly by 12?
  18. 18.What is the smallest number you must take away from 526 so that it divides exactly by 13?
  19. 19.What is the smallest number you must take away from 923 so that it divides exactly by 7?
  20. 20.How many factors does 46 have?
  21. 21.What is the smallest number you must take away from 591 so that it divides exactly by 12?
  22. 22.Which of these numbers divides exactly by 4? (a) 5102 (b) 3473 (c) 6199 (d) 3800
  23. 23.How many factors does 29 have?
  24. 24.Which of these numbers divides exactly by 6? (a) 8793 (b) 1811 (c) 7102 (d) 1542
  25. 25.What is the smallest number you must add to 152 so that it divides exactly by 7?
  26. 26.How many factors does 91 have?
  27. 27.How many factors does 30 have?
  28. 28.How many factors does 55 have?
  29. 29.What is the smallest number you must take away from 847 so that it divides exactly by 6?
  30. 30.How many factors does 82 have?
  31. 31.How many factors does 95 have?
  32. 32.What is the smallest number you must take away from 790 so that it divides exactly by 11?
  33. 33.What is the smallest number you must add to 994 so that it divides exactly by 11?
  34. 34.Which of these numbers divides exactly by 3? (a) 2965 (b) 4142 (c) 2767 (d) 4476
  35. 35.What is the smallest number you must take away from 326 so that it divides exactly by 8?
  36. 36.Which of these numbers divides exactly by 4? (a) 3964 (b) 1646 (c) 1013 (d) 5343
  37. 37.What is the smallest number you must add to 827 so that it divides exactly by 3?
  38. 38.What is the smallest number you must add to 298 so that it divides exactly by 4?
  39. 39.Which of these numbers divides exactly by 4? (a) 7064 (b) 6778 (c) 4637 (d) 6719
  40. 40.How many factors does 14 have?

Answer key

  1. 2304
  2. 1
  3. 4
  4. 8
  5. 8
  6. 5742
  7. 3
  8. 4
  9. 4906
  10. 3
  11. 2
  12. 3
  13. 2
  14. 3
  15. 4
  16. 2
  17. 7
  18. 6
  19. 6
  20. 4
  21. 3
  22. 3800
  23. 2
  24. 1542
  25. 2
  26. 4
  27. 8
  28. 4
  29. 1
  30. 4
  31. 4
  32. 9
  33. 7
  34. 4476
  35. 6
  36. 3964
  37. 1
  38. 2
  39. 7064
  40. 4

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