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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 108 · 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 34 have?
  2. 2.What is the smallest number you must add to 873 so that it divides exactly by 4?
  3. 3.How many factors does 68 have?
  4. 4.What is the smallest number you must add to 962 so that it divides exactly by 8?
  5. 5.What is the smallest number you must add to 613 so that it divides exactly by 9?
  6. 6.What is the smallest number you must add to 914 so that it divides exactly by 3?
  7. 7.What is the smallest number you must take away from 647 so that it divides exactly by 12?
  8. 8.How many factors does 90 have?
  9. 9.How many factors does 12 have?
  10. 10.What is the smallest number you must add to 611 so that it divides exactly by 8?
  11. 11.What is the smallest number you must add to 947 so that it divides exactly by 9?
  12. 12.What is the smallest number you must add to 895 so that it divides exactly by 8?
  13. 13.What is the smallest number you must add to 701 so that it divides exactly by 12?
  14. 14.How many factors does 61 have?
  15. 15.What is the smallest number you must add to 484 so that it divides exactly by 9?
  16. 16.What is the smallest number you must take away from 504 so that it divides exactly by 13?
  17. 17.How many factors does 26 have?
  18. 18.Which of these numbers divides exactly by 8? (a) 6252 (b) 1936 (c) 8871 (d) 4767
  19. 19.What is the smallest number you must take away from 326 so that it divides exactly by 8?
  20. 20.Which of these numbers divides exactly by 8? (a) 2578 (b) 3686 (c) 8858 (d) 7456
  21. 21.How many factors does 65 have?
  22. 22.What is the smallest number you must take away from 705 so that it divides exactly by 9?
  23. 23.How many factors does 36 have?
  24. 24.What is the smallest number you must add to 842 so that it divides exactly by 11?
  25. 25.Which of these numbers divides exactly by 3? (a) 5924 (b) 7608 (c) 9835 (d) 7654
  26. 26.How many factors does 95 have?
  27. 27.How many factors does 28 have?
  28. 28.What is the smallest number you must add to 692 so that it divides exactly by 3?
  29. 29.How many factors does 88 have?
  30. 30.What is the smallest number you must add to 435 so that it divides exactly by 11?
  31. 31.What is the smallest number you must take away from 549 so that it divides exactly by 7?
  32. 32.How many factors does 62 have?
  33. 33.Which of these numbers divides exactly by 3? (a) 7364 (b) 1332 (c) 7453 (d) 6901
  34. 34.Which of these numbers divides exactly by 11? (a) 1769 (b) 1698 (c) 5794 (d) 5423
  35. 35.What is the smallest number you must take away from 251 so that it divides exactly by 4?
  36. 36.How many factors does 45 have?
  37. 37.Which of these numbers divides exactly by 3? (a) 6575 (b) 1696 (c) 6229 (d) 2298
  38. 38.Which of these numbers divides exactly by 6? (a) 3079 (b) 4875 (c) 1368 (d) 3272
  39. 39.How many factors does 64 have?
  40. 40.Which of these numbers divides exactly by 8? (a) 9383 (b) 1777 (c) 1424 (d) 6405

Answer key

  1. 4
  2. 3
  3. 6
  4. 6
  5. 8
  6. 1
  7. 11
  8. 12
  9. 6
  10. 5
  11. 7
  12. 1
  13. 7
  14. 2
  15. 2
  16. 10
  17. 4
  18. 1936
  19. 6
  20. 7456
  21. 4
  22. 3
  23. 9
  24. 5
  25. 7608
  26. 4
  27. 6
  28. 1
  29. 8
  30. 5
  31. 3
  32. 4
  33. 1332
  34. 5423
  35. 3
  36. 6
  37. 2298
  38. 1368
  39. 7
  40. 1424

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