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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 324 · 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 23 have?
  2. 2.What is the smallest number you must take away from 271 so that it divides exactly by 6?
  3. 3.What is the smallest number you must add to 853 so that it divides exactly by 9?
  4. 4.What is the smallest number you must take away from 196 so that it divides exactly by 12?
  5. 5.What is the smallest number you must add to 543 so that it divides exactly by 12?
  6. 6.How many factors does 46 have?
  7. 7.What is the smallest number you must add to 901 so that it divides exactly by 12?
  8. 8.Which of these numbers divides exactly by 3? (a) 4679 (b) 4504 (c) 2286 (d) 5660
  9. 9.How many factors does 57 have?
  10. 10.What is the smallest number you must add to 532 so that it divides exactly by 3?
  11. 11.What is the smallest number you must add to 550 so that it divides exactly by 3?
  12. 12.How many factors does 35 have?
  13. 13.What is the smallest number you must take away from 807 so that it divides exactly by 11?
  14. 14.How many factors does 95 have?
  15. 15.What is the smallest number you must take away from 561 so that it divides exactly by 13?
  16. 16.Which of these numbers divides exactly by 11? (a) 1165 (b) 1815 (c) 5278 (d) 3640
  17. 17.What is the smallest number you must add to 804 so that it divides exactly by 7?
  18. 18.What is the smallest number you must take away from 659 so that it divides exactly by 11?
  19. 19.Which of these numbers divides exactly by 4? (a) 2407 (b) 5600 (c) 2978 (d) 7646
  20. 20.Which of these numbers divides exactly by 3? (a) 2238 (b) 4142 (c) 3421 (d) 9766
  21. 21.What is the smallest number you must take away from 583 so that it divides exactly by 3?
  22. 22.How many factors does 14 have?
  23. 23.How many factors does 87 have?
  24. 24.Which of these numbers divides exactly by 8? (a) 2777 (b) 3473 (c) 3027 (d) 6136
  25. 25.Which of these numbers divides exactly by 3? (a) 6593 (b) 2475 (c) 9836 (d) 2783
  26. 26.What is the smallest number you must add to 748 so that it divides exactly by 8?
  27. 27.How many factors does 21 have?
  28. 28.What is the smallest number you must take away from 271 so that it divides exactly by 4?
  29. 29.What is the smallest number you must take away from 183 so that it divides exactly by 4?
  30. 30.What is the smallest number you must take away from 465 so that it divides exactly by 4?
  31. 31.What is the smallest number you must take away from 682 so that it divides exactly by 6?
  32. 32.What is the smallest number you must take away from 350 so that it divides exactly by 12?
  33. 33.How many factors does 22 have?
  34. 34.Which of these numbers divides exactly by 11? (a) 1504 (b) 9691 (c) 9847 (d) 9533
  35. 35.Which of these numbers divides exactly by 6? (a) 1464 (b) 5228 (c) 9962 (d) 2036
  36. 36.What is the smallest number you must take away from 162 so that it divides exactly by 8?
  37. 37.How many factors does 32 have?
  38. 38.What is the smallest number you must add to 625 so that it divides exactly by 9?
  39. 39.Which of these numbers divides exactly by 8? (a) 2013 (b) 9942 (c) 9712 (d) 9321
  40. 40.Which of these numbers divides exactly by 11? (a) 4820 (b) 6666 (c) 4692 (d) 7493

Answer key

  1. 2
  2. 1
  3. 2
  4. 4
  5. 9
  6. 4
  7. 11
  8. 2286
  9. 4
  10. 2
  11. 2
  12. 4
  13. 4
  14. 4
  15. 2
  16. 1815
  17. 1
  18. 10
  19. 5600
  20. 2238
  21. 1
  22. 4
  23. 4
  24. 6136
  25. 2475
  26. 4
  27. 4
  28. 3
  29. 3
  30. 1
  31. 4
  32. 2
  33. 4
  34. 9691
  35. 1464
  36. 2
  37. 6
  38. 5
  39. 9712
  40. 6666

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