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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 85 · 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 take away from 280 so that it divides exactly by 12?
  2. 2.Which of these numbers divides exactly by 3? (a) 2598 (b) 4217 (c) 9314 (d) 4330
  3. 3.How many factors does 15 have?
  4. 4.What is the smallest number you must take away from 582 so that it divides exactly by 4?
  5. 5.What is the smallest number you must add to 629 so that it divides exactly by 6?
  6. 6.What is the smallest number you must take away from 730 so that it divides exactly by 3?
  7. 7.What is the smallest number you must take away from 455 so that it divides exactly by 6?
  8. 8.What is the smallest number you must take away from 775 so that it divides exactly by 12?
  9. 9.What is the smallest number you must add to 578 so that it divides exactly by 8?
  10. 10.How many factors does 63 have?
  11. 11.How many factors does 78 have?
  12. 12.Which of these numbers divides exactly by 3? (a) 7456 (b) 5915 (c) 5499 (d) 6844
  13. 13.What is the smallest number you must add to 974 so that it divides exactly by 7?
  14. 14.How many factors does 83 have?
  15. 15.What is the smallest number you must add to 943 so that it divides exactly by 3?
  16. 16.How many factors does 14 have?
  17. 17.Which of these numbers divides exactly by 6? (a) 7679 (b) 3083 (c) 4008 (d) 7297
  18. 18.How many factors does 74 have?
  19. 19.Which of these numbers divides exactly by 4? (a) 8601 (b) 3618 (c) 9352 (d) 3819
  20. 20.How many factors does 77 have?
  21. 21.What is the smallest number you must add to 834 so that it divides exactly by 9?
  22. 22.What is the smallest number you must add to 250 so that it divides exactly by 7?
  23. 23.What is the smallest number you must add to 410 so that it divides exactly by 8?
  24. 24.How many factors does 80 have?
  25. 25.What is the smallest number you must take away from 162 so that it divides exactly by 7?
  26. 26.What is the smallest number you must add to 220 so that it divides exactly by 12?
  27. 27.What is the smallest number you must add to 202 so that it divides exactly by 11?
  28. 28.What is the smallest number you must add to 143 so that it divides exactly by 9?
  29. 29.What is the smallest number you must take away from 196 so that it divides exactly by 12?
  30. 30.What is the smallest number you must add to 277 so that it divides exactly by 12?
  31. 31.What is the smallest number you must add to 989 so that it divides exactly by 9?
  32. 32.What is the smallest number you must take away from 808 so that it divides exactly by 3?
  33. 33.How many factors does 97 have?
  34. 34.How many factors does 13 have?
  35. 35.How many factors does 89 have?
  36. 36.How many factors does 82 have?
  37. 37.Which of these numbers divides exactly by 11? (a) 5538 (b) 9556 (c) 3152 (d) 2343
  38. 38.What is the smallest number you must add to 445 so that it divides exactly by 11?
  39. 39.What is the smallest number you must take away from 909 so that it divides exactly by 6?
  40. 40.How many factors does 60 have?

Answer key

  1. 4
  2. 2598
  3. 4
  4. 2
  5. 1
  6. 1
  7. 5
  8. 7
  9. 6
  10. 6
  11. 8
  12. 5499
  13. 6
  14. 2
  15. 2
  16. 4
  17. 4008
  18. 4
  19. 9352
  20. 4
  21. 3
  22. 2
  23. 6
  24. 10
  25. 1
  26. 8
  27. 7
  28. 1
  29. 4
  30. 11
  31. 1
  32. 1
  33. 2
  34. 2
  35. 2
  36. 4
  37. 2343
  38. 6
  39. 3
  40. 12

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