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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 77 · 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 take away from 863 so that it divides exactly by 12?
  2. 2.What is the smallest number you must take away from 151 so that it divides exactly by 7?
  3. 3.What is the smallest number you must add to 663 so that it divides exactly by 6?
  4. 4.What is the smallest number you must take away from 604 so that it divides exactly by 11?
  5. 5.What is the smallest number you must add to 518 so that it divides exactly by 12?
  6. 6.What is the smallest number you must add to 508 so that it divides exactly by 13?
  7. 7.What is the smallest number you must take away from 533 so that it divides exactly by 11?
  8. 8.What is the smallest number you must add to 869 so that it divides exactly by 13?
  9. 9.What is the smallest number you must take away from 278 so that it divides exactly by 9?
  10. 10.How many factors does 75 have?
  11. 11.What is the smallest number you must add to 460 so that it divides exactly by 9?
  12. 12.Which of these numbers divides exactly by 8? (a) 8082 (b) 8552 (c) 7342 (d) 9194
  13. 13.What is the smallest number you must add to 923 so that it divides exactly by 9?
  14. 14.Which of these numbers divides exactly by 3? (a) 2822 (b) 1680 (c) 7469 (d) 7247
  15. 15.What is the smallest number you must add to 332 so that it divides exactly by 13?
  16. 16.What is the smallest number you must add to 162 so that it divides exactly by 8?
  17. 17.How many factors does 30 have?
  18. 18.What is the smallest number you must take away from 585 so that it divides exactly by 4?
  19. 19.What is the smallest number you must take away from 428 so that it divides exactly by 12?
  20. 20.How many factors does 96 have?
  21. 21.What is the smallest number you must add to 387 so that it divides exactly by 11?
  22. 22.What is the smallest number you must add to 433 so that it divides exactly by 4?
  23. 23.How many factors does 44 have?
  24. 24.How many factors does 59 have?
  25. 25.What is the smallest number you must add to 580 so that it divides exactly by 6?
  26. 26.Which of these numbers divides exactly by 3? (a) 5116 (b) 3829 (c) 6276 (d) 1994
  27. 27.What is the smallest number you must take away from 849 so that it divides exactly by 7?
  28. 28.What is the smallest number you must add to 742 so that it divides exactly by 4?
  29. 29.What is the smallest number you must add to 922 so that it divides exactly by 8?
  30. 30.Which of these numbers divides exactly by 6? (a) 7367 (b) 2772 (c) 3488 (d) 8779
  31. 31.What is the smallest number you must add to 319 so that it divides exactly by 9?
  32. 32.What is the smallest number you must add to 779 so that it divides exactly by 13?
  33. 33.What is the smallest number you must add to 836 so that it divides exactly by 3?
  34. 34.What is the smallest number you must add to 155 so that it divides exactly by 8?
  35. 35.What is the smallest number you must take away from 127 so that it divides exactly by 11?
  36. 36.What is the smallest number you must take away from 107 so that it divides exactly by 12?
  37. 37.How many factors does 81 have?
  38. 38.How many factors does 35 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 2923 (b) 2040 (c) 8785 (d) 8803
  40. 40.Which of these numbers divides exactly by 4? (a) 4170 (b) 1396 (c) 4833 (d) 8251

Answer key

  1. 11
  2. 4
  3. 3
  4. 10
  5. 10
  6. 12
  7. 5
  8. 2
  9. 8
  10. 6
  11. 8
  12. 8552
  13. 4
  14. 1680
  15. 6
  16. 6
  17. 8
  18. 1
  19. 8
  20. 12
  21. 9
  22. 3
  23. 6
  24. 2
  25. 2
  26. 6276
  27. 2
  28. 2
  29. 6
  30. 2772
  31. 5
  32. 1
  33. 1
  34. 5
  35. 6
  36. 11
  37. 5
  38. 4
  39. 2040
  40. 1396

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