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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 177 · 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.Which of these numbers divides exactly by 6? (a) 3224 (b) 7878 (c) 2303 (d) 4831
  3. 3.What is the smallest number you must add to 358 so that it divides exactly by 6?
  4. 4.What is the smallest number you must take away from 241 so that it divides exactly by 3?
  5. 5.How many factors does 55 have?
  6. 6.How many factors does 83 have?
  7. 7.What is the smallest number you must take away from 204 so that it divides exactly by 11?
  8. 8.What is the smallest number you must add to 956 so that it divides exactly by 12?
  9. 9.What is the smallest number you must add to 801 so that it divides exactly by 12?
  10. 10.What is the smallest number you must take away from 722 so that it divides exactly by 4?
  11. 11.Which of these numbers divides exactly by 6? (a) 2259 (b) 9720 (c) 6826 (d) 3191
  12. 12.Which of these numbers divides exactly by 3? (a) 8881 (b) 1075 (c) 9285 (d) 9809
  13. 13.What is the smallest number you must take away from 899 so that it divides exactly by 13?
  14. 14.What is the smallest number you must add to 725 so that it divides exactly by 13?
  15. 15.How many factors does 12 have?
  16. 16.Which of these numbers divides exactly by 8? (a) 3523 (b) 3025 (c) 3810 (d) 1536
  17. 17.What is the smallest number you must add to 548 so that it divides exactly by 11?
  18. 18.What is the smallest number you must add to 823 so that it divides exactly by 3?
  19. 19.How many factors does 33 have?
  20. 20.Which of these numbers divides exactly by 6? (a) 8915 (b) 6482 (c) 3960 (d) 2822
  21. 21.What is the smallest number you must take away from 926 so that it divides exactly by 7?
  22. 22.Which of these numbers divides exactly by 6? (a) 2067 (b) 1099 (c) 3709 (d) 6432
  23. 23.How many factors does 19 have?
  24. 24.What is the smallest number you must add to 879 so that it divides exactly by 8?
  25. 25.What is the smallest number you must add to 320 so that it divides exactly by 13?
  26. 26.What is the smallest number you must add to 491 so that it divides exactly by 7?
  27. 27.What is the smallest number you must add to 519 so that it divides exactly by 11?
  28. 28.What is the smallest number you must add to 502 so that it divides exactly by 8?
  29. 29.What is the smallest number you must take away from 663 so that it divides exactly by 9?
  30. 30.What is the smallest number you must add to 205 so that it divides exactly by 8?
  31. 31.What is the smallest number you must add to 955 so that it divides exactly by 11?
  32. 32.What is the smallest number you must add to 953 so that it divides exactly by 12?
  33. 33.What is the smallest number you must take away from 511 so that it divides exactly by 9?
  34. 34.What is the smallest number you must add to 854 so that it divides exactly by 13?
  35. 35.How many factors does 59 have?
  36. 36.How many factors does 17 have?
  37. 37.What is the smallest number you must add to 690 so that it divides exactly by 9?
  38. 38.What is the smallest number you must take away from 928 so that it divides exactly by 12?
  39. 39.What is the smallest number you must add to 378 so that it divides exactly by 11?
  40. 40.How many factors does 50 have?

Answer key

  1. 6
  2. 7878
  3. 2
  4. 1
  5. 4
  6. 2
  7. 6
  8. 4
  9. 3
  10. 2
  11. 9720
  12. 9285
  13. 2
  14. 3
  15. 6
  16. 1536
  17. 2
  18. 2
  19. 4
  20. 3960
  21. 2
  22. 6432
  23. 2
  24. 1
  25. 5
  26. 6
  27. 9
  28. 2
  29. 6
  30. 3
  31. 2
  32. 7
  33. 7
  34. 4
  35. 2
  36. 2
  37. 3
  38. 4
  39. 7
  40. 6

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