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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 284 · 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 851 so that it divides exactly by 12?
  2. 2.How many factors does 95 have?
  3. 3.What is the smallest number you must add to 159 so that it divides exactly by 7?
  4. 4.Which of these numbers divides exactly by 9? (a) 3178 (b) 5976 (c) 6396 (d) 3883
  5. 5.How many factors does 81 have?
  6. 6.Which of these numbers divides exactly by 9? (a) 5918 (b) 4243 (c) 3605 (d) 1620
  7. 7.What is the smallest number you must add to 337 so that it divides exactly by 13?
  8. 8.How many factors does 52 have?
  9. 9.What is the smallest number you must add to 783 so that it divides exactly by 7?
  10. 10.How many factors does 31 have?
  11. 11.What is the smallest number you must take away from 989 so that it divides exactly by 11?
  12. 12.What is the smallest number you must take away from 856 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 340 so that it divides exactly by 8?
  14. 14.How many factors does 99 have?
  15. 15.How many factors does 60 have?
  16. 16.How many factors does 16 have?
  17. 17.Which of these numbers divides exactly by 11? (a) 5951 (b) 9489 (c) 1919 (d) 8353
  18. 18.Which of these numbers divides exactly by 8? (a) 2316 (b) 2512 (c) 4157 (d) 6147
  19. 19.Which of these numbers divides exactly by 3? (a) 5568 (b) 8311 (c) 4510 (d) 2702
  20. 20.How many factors does 28 have?
  21. 21.What is the smallest number you must add to 782 so that it divides exactly by 3?
  22. 22.What is the smallest number you must add to 429 so that it divides exactly by 8?
  23. 23.What is the smallest number you must add to 815 so that it divides exactly by 4?
  24. 24.Which of these numbers divides exactly by 3? (a) 5487 (b) 6244 (c) 9676 (d) 1178
  25. 25.What is the smallest number you must take away from 259 so that it divides exactly by 6?
  26. 26.What is the smallest number you must take away from 649 so that it divides exactly by 9?
  27. 27.How many factors does 43 have?
  28. 28.How many factors does 55 have?
  29. 29.How many factors does 93 have?
  30. 30.How many factors does 92 have?
  31. 31.How many factors does 91 have?
  32. 32.What is the smallest number you must add to 677 so that it divides exactly by 4?
  33. 33.What is the smallest number you must take away from 169 so that it divides exactly by 12?
  34. 34.What is the smallest number you must add to 382 so that it divides exactly by 4?
  35. 35.What is the smallest number you must take away from 102 so that it divides exactly by 11?
  36. 36.How many factors does 71 have?
  37. 37.What is the smallest number you must add to 673 so that it divides exactly by 3?
  38. 38.Which of these numbers divides exactly by 11? (a) 8221 (b) 3928 (c) 4734 (d) 6798
  39. 39.How many factors does 77 have?
  40. 40.Which of these numbers divides exactly by 9? (a) 6588 (b) 5725 (c) 4330 (d) 5642

Answer key

  1. 1
  2. 4
  3. 2
  4. 5976
  5. 5
  6. 1620
  7. 1
  8. 6
  9. 1
  10. 2
  11. 10
  12. 11
  13. 4
  14. 6
  15. 12
  16. 5
  17. 5951
  18. 2512
  19. 5568
  20. 6
  21. 1
  22. 3
  23. 1
  24. 5487
  25. 1
  26. 1
  27. 2
  28. 4
  29. 4
  30. 6
  31. 4
  32. 3
  33. 1
  34. 2
  35. 3
  36. 2
  37. 2
  38. 6798
  39. 4
  40. 6588

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