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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 314 · 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 89 have?
  2. 2.What is the smallest number you must add to 695 so that it divides exactly by 4?
  3. 3.How many factors does 20 have?
  4. 4.Which of these numbers divides exactly by 4? (a) 7538 (b) 1301 (c) 6660 (d) 5790
  5. 5.What is the smallest number you must take away from 971 so that it divides exactly by 8?
  6. 6.What is the smallest number you must add to 638 so that it divides exactly by 3?
  7. 7.Which of these numbers divides exactly by 9? (a) 5048 (b) 5447 (c) 7656 (d) 7353
  8. 8.Which of these numbers divides exactly by 11? (a) 4759 (b) 1664 (c) 8520 (d) 6424
  9. 9.How many factors does 47 have?
  10. 10.What is the smallest number you must add to 221 so that it divides exactly by 12?
  11. 11.What is the smallest number you must take away from 739 so that it divides exactly by 11?
  12. 12.How many factors does 77 have?
  13. 13.What is the smallest number you must add to 403 so that it divides exactly by 6?
  14. 14.What is the smallest number you must add to 363 so that it divides exactly by 12?
  15. 15.Which of these numbers divides exactly by 4? (a) 3673 (b) 6803 (c) 2305 (d) 5268
  16. 16.How many factors does 62 have?
  17. 17.How many factors does 60 have?
  18. 18.How many factors does 63 have?
  19. 19.What is the smallest number you must add to 994 so that it divides exactly by 6?
  20. 20.How many factors does 84 have?
  21. 21.How many factors does 46 have?
  22. 22.Which of these numbers divides exactly by 3? (a) 9140 (b) 7294 (c) 2335 (d) 4884
  23. 23.Which of these numbers divides exactly by 6? (a) 3846 (b) 6593 (c) 7112 (d) 3815
  24. 24.How many factors does 68 have?
  25. 25.What is the smallest number you must take away from 731 so that it divides exactly by 8?
  26. 26.What is the smallest number you must add to 859 so that it divides exactly by 9?
  27. 27.How many factors does 69 have?
  28. 28.How many factors does 99 have?
  29. 29.What is the smallest number you must take away from 670 so that it divides exactly by 9?
  30. 30.What is the smallest number you must take away from 873 so that it divides exactly by 7?
  31. 31.What is the smallest number you must take away from 194 so that it divides exactly by 13?
  32. 32.What is the smallest number you must add to 318 so that it divides exactly by 13?
  33. 33.What is the smallest number you must take away from 658 so that it divides exactly by 12?
  34. 34.What is the smallest number you must add to 154 so that it divides exactly by 4?
  35. 35.What is the smallest number you must take away from 573 so that it divides exactly by 8?
  36. 36.How many factors does 44 have?
  37. 37.How many factors does 90 have?
  38. 38.Which of these numbers divides exactly by 9? (a) 3614 (b) 3762 (c) 1631 (d) 2776
  39. 39.Which of these numbers divides exactly by 8? (a) 2023 (b) 6485 (c) 8737 (d) 8080
  40. 40.What is the smallest number you must add to 707 so that it divides exactly by 12?

Answer key

  1. 2
  2. 1
  3. 6
  4. 6660
  5. 3
  6. 1
  7. 7353
  8. 6424
  9. 2
  10. 7
  11. 2
  12. 4
  13. 5
  14. 9
  15. 5268
  16. 4
  17. 12
  18. 6
  19. 2
  20. 12
  21. 4
  22. 4884
  23. 3846
  24. 6
  25. 3
  26. 5
  27. 4
  28. 6
  29. 4
  30. 5
  31. 12
  32. 7
  33. 10
  34. 2
  35. 5
  36. 6
  37. 12
  38. 3762
  39. 8080
  40. 1

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