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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 126 · 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 add to 455 so that it divides exactly by 4?
  2. 2.What is the smallest number you must add to 926 so that it divides exactly by 4?
  3. 3.What is the smallest number you must take away from 394 so that it divides exactly by 9?
  4. 4.How many factors does 69 have?
  5. 5.What is the smallest number you must add to 134 so that it divides exactly by 12?
  6. 6.Which of these numbers divides exactly by 11? (a) 4412 (b) 7227 (c) 5910 (d) 2785
  7. 7.What is the smallest number you must take away from 682 so that it divides exactly by 12?
  8. 8.What is the smallest number you must add to 733 so that it divides exactly by 3?
  9. 9.Which of these numbers divides exactly by 11? (a) 2239 (b) 3909 (c) 5016 (d) 2137
  10. 10.What is the smallest number you must take away from 663 so that it divides exactly by 12?
  11. 11.How many factors does 60 have?
  12. 12.What is the smallest number you must take away from 151 so that it divides exactly by 7?
  13. 13.What is the smallest number you must add to 394 so that it divides exactly by 9?
  14. 14.What is the smallest number you must take away from 467 so that it divides exactly by 9?
  15. 15.What is the smallest number you must take away from 823 so that it divides exactly by 13?
  16. 16.What is the smallest number you must take away from 776 so that it divides exactly by 11?
  17. 17.Which of these numbers divides exactly by 3? (a) 8012 (b) 5482 (c) 7883 (d) 1824
  18. 18.What is the smallest number you must add to 801 so that it divides exactly by 7?
  19. 19.What is the smallest number you must take away from 673 so that it divides exactly by 12?
  20. 20.How many factors does 47 have?
  21. 21.What is the smallest number you must add to 368 so that it divides exactly by 12?
  22. 22.What is the smallest number you must add to 918 so that it divides exactly by 8?
  23. 23.What is the smallest number you must take away from 896 so that it divides exactly by 13?
  24. 24.How many factors does 65 have?
  25. 25.Which of these numbers divides exactly by 11? (a) 6732 (b) 9089 (c) 8999 (d) 6051
  26. 26.What is the smallest number you must take away from 564 so that it divides exactly by 9?
  27. 27.How many factors does 98 have?
  28. 28.How many factors does 68 have?
  29. 29.How many factors does 53 have?
  30. 30.How many factors does 20 have?
  31. 31.What is the smallest number you must add to 197 so that it divides exactly by 11?
  32. 32.What is the smallest number you must take away from 953 so that it divides exactly by 12?
  33. 33.What is the smallest number you must take away from 958 so that it divides exactly by 13?
  34. 34.How many factors does 62 have?
  35. 35.What is the smallest number you must take away from 940 so that it divides exactly by 8?
  36. 36.Which of these numbers divides exactly by 3? (a) 4067 (b) 2934 (c) 8071 (d) 6686
  37. 37.Which of these numbers divides exactly by 8? (a) 2376 (b) 1105 (c) 7622 (d) 5349
  38. 38.Which of these numbers divides exactly by 9? (a) 3762 (b) 5078 (c) 1608 (d) 5465
  39. 39.Which of these numbers divides exactly by 9? (a) 6849 (b) 3118 (c) 5581 (d) 5453
  40. 40.How many factors does 12 have?

Answer key

  1. 1
  2. 2
  3. 7
  4. 4
  5. 10
  6. 7227
  7. 10
  8. 2
  9. 5016
  10. 3
  11. 12
  12. 4
  13. 2
  14. 8
  15. 4
  16. 6
  17. 1824
  18. 4
  19. 1
  20. 2
  21. 4
  22. 2
  23. 12
  24. 4
  25. 6732
  26. 6
  27. 6
  28. 6
  29. 2
  30. 6
  31. 1
  32. 5
  33. 9
  34. 4
  35. 4
  36. 2934
  37. 2376
  38. 3762
  39. 6849
  40. 6

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