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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 207 · 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 6? (a) 1037 (b) 5812 (c) 6612 (d) 5458
  2. 2.How many factors does 21 have?
  3. 3.Which of these numbers divides exactly by 3? (a) 2532 (b) 7177 (c) 6782 (d) 7594
  4. 4.How many factors does 65 have?
  5. 5.What is the smallest number you must add to 737 so that it divides exactly by 8?
  6. 6.How many factors does 60 have?
  7. 7.Which of these numbers divides exactly by 3? (a) 9388 (b) 8268 (c) 1115 (d) 8654
  8. 8.What is the smallest number you must add to 296 so that it divides exactly by 7?
  9. 9.How many factors does 43 have?
  10. 10.What is the smallest number you must add to 733 so that it divides exactly by 13?
  11. 11.What is the smallest number you must take away from 426 so that it divides exactly by 7?
  12. 12.Which of these numbers divides exactly by 3? (a) 2661 (b) 1291 (c) 2273 (d) 3325
  13. 13.How many factors does 74 have?
  14. 14.What is the smallest number you must add to 313 so that it divides exactly by 6?
  15. 15.How many factors does 82 have?
  16. 16.What is the smallest number you must add to 658 so that it divides exactly by 12?
  17. 17.What is the smallest number you must add to 493 so that it divides exactly by 11?
  18. 18.What is the smallest number you must take away from 638 so that it divides exactly by 9?
  19. 19.Which of these numbers divides exactly by 4? (a) 3038 (b) 6217 (c) 7383 (d) 3504
  20. 20.Which of these numbers divides exactly by 4? (a) 7770 (b) 6130 (c) 8630 (d) 2772
  21. 21.How many factors does 68 have?
  22. 22.What is the smallest number you must take away from 909 so that it divides exactly by 7?
  23. 23.What is the smallest number you must take away from 383 so that it divides exactly by 6?
  24. 24.How many factors does 85 have?
  25. 25.Which of these numbers divides exactly by 4? (a) 8771 (b) 9958 (c) 3311 (d) 1296
  26. 26.Which of these numbers divides exactly by 11? (a) 5536 (b) 7810 (c) 2583 (d) 1646
  27. 27.What is the smallest number you must add to 127 so that it divides exactly by 4?
  28. 28.What is the smallest number you must take away from 687 so that it divides exactly by 8?
  29. 29.Which of these numbers divides exactly by 11? (a) 2787 (b) 4452 (c) 6908 (d) 1909
  30. 30.How many factors does 58 have?
  31. 31.What is the smallest number you must add to 642 so that it divides exactly by 4?
  32. 32.How many factors does 56 have?
  33. 33.Which of these numbers divides exactly by 8? (a) 1913 (b) 9032 (c) 1175 (d) 4506
  34. 34.How many factors does 72 have?
  35. 35.How many factors does 30 have?
  36. 36.How many factors does 36 have?
  37. 37.Which of these numbers divides exactly by 3? (a) 8166 (b) 9082 (c) 4528 (d) 4372
  38. 38.What is the smallest number you must take away from 801 so that it divides exactly by 8?
  39. 39.How many factors does 69 have?
  40. 40.What is the smallest number you must add to 887 so that it divides exactly by 11?

Answer key

  1. 6612
  2. 4
  3. 2532
  4. 4
  5. 7
  6. 12
  7. 8268
  8. 5
  9. 2
  10. 8
  11. 6
  12. 2661
  13. 4
  14. 5
  15. 4
  16. 2
  17. 2
  18. 8
  19. 3504
  20. 2772
  21. 6
  22. 6
  23. 5
  24. 4
  25. 1296
  26. 7810
  27. 1
  28. 7
  29. 6908
  30. 4
  31. 2
  32. 8
  33. 9032
  34. 12
  35. 8
  36. 9
  37. 8166
  38. 1
  39. 4
  40. 4

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