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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 231 · 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.Which of these numbers divides exactly by 4? (a) 7178 (b) 9142 (c) 9628 (d) 5821
  2. 2.How many factors does 96 have?
  3. 3.What is the smallest number you must take away from 402 so that it divides exactly by 12?
  4. 4.Which of these numbers divides exactly by 8? (a) 8304 (b) 6801 (c) 5433 (d) 3455
  5. 5.How many factors does 17 have?
  6. 6.What is the smallest number you must add to 226 so that it divides exactly by 3?
  7. 7.What is the smallest number you must add to 121 so that it divides exactly by 7?
  8. 8.What is the smallest number you must take away from 687 so that it divides exactly by 4?
  9. 9.How many factors does 43 have?
  10. 10.How many factors does 72 have?
  11. 11.What is the smallest number you must take away from 391 so that it divides exactly by 9?
  12. 12.Which of these numbers divides exactly by 8? (a) 3060 (b) 9138 (c) 7225 (d) 9192
  13. 13.What is the smallest number you must add to 656 so that it divides exactly by 7?
  14. 14.Which of these numbers divides exactly by 9? (a) 6380 (b) 3257 (c) 5229 (d) 4524
  15. 15.How many factors does 46 have?
  16. 16.What is the smallest number you must add to 297 so that it divides exactly by 4?
  17. 17.How many factors does 91 have?
  18. 18.What is the smallest number you must add to 131 so that it divides exactly by 9?
  19. 19.What is the smallest number you must take away from 158 so that it divides exactly by 3?
  20. 20.How many factors does 38 have?
  21. 21.What is the smallest number you must add to 221 so that it divides exactly by 4?
  22. 22.How many factors does 25 have?
  23. 23.How many factors does 37 have?
  24. 24.What is the smallest number you must take away from 441 so that it divides exactly by 4?
  25. 25.How many factors does 45 have?
  26. 26.How many factors does 78 have?
  27. 27.What is the smallest number you must add to 562 so that it divides exactly by 9?
  28. 28.What is the smallest number you must take away from 590 so that it divides exactly by 11?
  29. 29.What is the smallest number you must add to 757 so that it divides exactly by 13?
  30. 30.How many factors does 79 have?
  31. 31.What is the smallest number you must add to 816 so that it divides exactly by 9?
  32. 32.What is the smallest number you must add to 357 so that it divides exactly by 13?
  33. 33.What is the smallest number you must take away from 244 so that it divides exactly by 9?
  34. 34.What is the smallest number you must take away from 964 so that it divides exactly by 3?
  35. 35.What is the smallest number you must add to 652 so that it divides exactly by 9?
  36. 36.Which of these numbers divides exactly by 3? (a) 7827 (b) 7649 (c) 4681 (d) 5467
  37. 37.What is the smallest number you must add to 167 so that it divides exactly by 7?
  38. 38.What is the smallest number you must add to 754 so that it divides exactly by 9?
  39. 39.Which of these numbers divides exactly by 11? (a) 3025 (b) 7254 (c) 3397 (d) 1482
  40. 40.Which of these numbers divides exactly by 6? (a) 3074 (b) 2916 (c) 9243 (d) 4693

Answer key

  1. 9628
  2. 12
  3. 6
  4. 8304
  5. 2
  6. 2
  7. 5
  8. 3
  9. 2
  10. 12
  11. 4
  12. 9192
  13. 2
  14. 5229
  15. 4
  16. 3
  17. 4
  18. 4
  19. 2
  20. 4
  21. 3
  22. 3
  23. 2
  24. 1
  25. 6
  26. 8
  27. 5
  28. 7
  29. 10
  30. 2
  31. 3
  32. 7
  33. 1
  34. 1
  35. 5
  36. 7827
  37. 1
  38. 2
  39. 3025
  40. 2916

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