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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 289 · 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 45 have?
  2. 2.How many factors does 51 have?
  3. 3.Which of these numbers divides exactly by 11? (a) 9368 (b) 3492 (c) 9845 (d) 5361
  4. 4.What is the smallest number you must add to 396 so that it divides exactly by 13?
  5. 5.Which of these numbers divides exactly by 6? (a) 9907 (b) 8663 (c) 3659 (d) 5832
  6. 6.What is the smallest number you must add to 440 so that it divides exactly by 12?
  7. 7.How many factors does 29 have?
  8. 8.Which of these numbers divides exactly by 3? (a) 9903 (b) 2656 (c) 8437 (d) 2132
  9. 9.Which of these numbers divides exactly by 4? (a) 5282 (b) 9692 (c) 3666 (d) 3069
  10. 10.What is the smallest number you must take away from 362 so that it divides exactly by 4?
  11. 11.What is the smallest number you must take away from 111 so that it divides exactly by 13?
  12. 12.Which of these numbers divides exactly by 6? (a) 8445 (b) 2388 (c) 1750 (d) 1559
  13. 13.What is the smallest number you must add to 556 so that it divides exactly by 11?
  14. 14.How many factors does 30 have?
  15. 15.What is the smallest number you must take away from 753 so that it divides exactly by 12?
  16. 16.What is the smallest number you must add to 820 so that it divides exactly by 7?
  17. 17.Which of these numbers divides exactly by 8? (a) 9914 (b) 8321 (c) 7328 (d) 4855
  18. 18.What is the smallest number you must take away from 879 so that it divides exactly by 7?
  19. 19.How many factors does 32 have?
  20. 20.What is the smallest number you must add to 703 so that it divides exactly by 13?
  21. 21.How many factors does 40 have?
  22. 22.How many factors does 33 have?
  23. 23.Which of these numbers divides exactly by 3? (a) 1341 (b) 5141 (c) 1969 (d) 9617
  24. 24.Which of these numbers divides exactly by 11? (a) 2114 (b) 3467 (c) 2816 (d) 7286
  25. 25.How many factors does 61 have?
  26. 26.How many factors does 79 have?
  27. 27.How many factors does 68 have?
  28. 28.What is the smallest number you must take away from 318 so that it divides exactly by 9?
  29. 29.Which of these numbers divides exactly by 8? (a) 9102 (b) 6527 (c) 8974 (d) 7736
  30. 30.Which of these numbers divides exactly by 4? (a) 3871 (b) 9728 (c) 2450 (d) 9986
  31. 31.What is the smallest number you must add to 831 so that it divides exactly by 8?
  32. 32.How many factors does 75 have?
  33. 33.How many factors does 65 have?
  34. 34.How many factors does 46 have?
  35. 35.Which of these numbers divides exactly by 8? (a) 7245 (b) 3048 (c) 9763 (d) 3785
  36. 36.What is the smallest number you must add to 525 so that it divides exactly by 11?
  37. 37.Which of these numbers divides exactly by 4? (a) 7854 (b) 5817 (c) 9389 (d) 6848
  38. 38.What is the smallest number you must add to 366 so that it divides exactly by 11?
  39. 39.What is the smallest number you must take away from 175 so that it divides exactly by 11?
  40. 40.How many factors does 66 have?

Answer key

  1. 6
  2. 4
  3. 9845
  4. 7
  5. 5832
  6. 4
  7. 2
  8. 9903
  9. 9692
  10. 2
  11. 7
  12. 2388
  13. 5
  14. 8
  15. 9
  16. 6
  17. 7328
  18. 4
  19. 6
  20. 12
  21. 8
  22. 4
  23. 1341
  24. 2816
  25. 2
  26. 2
  27. 6
  28. 3
  29. 7736
  30. 9728
  31. 1
  32. 6
  33. 4
  34. 4
  35. 3048
  36. 3
  37. 6848
  38. 8
  39. 10
  40. 8

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