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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 155 · 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 97 have?
  2. 2.What is the smallest number you must take away from 570 so that it divides exactly by 9?
  3. 3.What is the smallest number you must take away from 736 so that it divides exactly by 11?
  4. 4.What is the smallest number you must add to 410 so that it divides exactly by 9?
  5. 5.How many factors does 18 have?
  6. 6.How many factors does 91 have?
  7. 7.What is the smallest number you must take away from 202 so that it divides exactly by 12?
  8. 8.Which of these numbers divides exactly by 3? (a) 6806 (b) 9871 (c) 3534 (d) 2572
  9. 9.Which of these numbers divides exactly by 4? (a) 5991 (b) 9888 (c) 3547 (d) 4379
  10. 10.Which of these numbers divides exactly by 3? (a) 9743 (b) 1184 (c) 6341 (d) 2055
  11. 11.What is the smallest number you must add to 318 so that it divides exactly by 4?
  12. 12.Which of these numbers divides exactly by 3? (a) 3577 (b) 3154 (c) 2045 (d) 7527
  13. 13.How many factors does 88 have?
  14. 14.How many factors does 34 have?
  15. 15.How many factors does 13 have?
  16. 16.How many factors does 99 have?
  17. 17.Which of these numbers divides exactly by 6? (a) 3819 (b) 3234 (c) 6278 (d) 3404
  18. 18.How many factors does 43 have?
  19. 19.How many factors does 80 have?
  20. 20.What is the smallest number you must take away from 346 so that it divides exactly by 13?
  21. 21.What is the smallest number you must add to 115 so that it divides exactly by 12?
  22. 22.What is the smallest number you must add to 244 so that it divides exactly by 3?
  23. 23.What is the smallest number you must add to 647 so that it divides exactly by 6?
  24. 24.What is the smallest number you must take away from 214 so that it divides exactly by 12?
  25. 25.How many factors does 96 have?
  26. 26.Which of these numbers divides exactly by 3? (a) 6411 (b) 5279 (c) 7907 (d) 3169
  27. 27.How many factors does 12 have?
  28. 28.What is the smallest number you must add to 530 so that it divides exactly by 11?
  29. 29.What is the smallest number you must take away from 404 so that it divides exactly by 13?
  30. 30.How many factors does 52 have?
  31. 31.How many factors does 40 have?
  32. 32.Which of these numbers divides exactly by 3? (a) 6005 (b) 3281 (c) 8806 (d) 8271
  33. 33.What is the smallest number you must add to 823 so that it divides exactly by 9?
  34. 34.How many factors does 78 have?
  35. 35.What is the smallest number you must add to 617 so that it divides exactly by 8?
  36. 36.Which of these numbers divides exactly by 8? (a) 9591 (b) 4079 (c) 3413 (d) 2144
  37. 37.Which of these numbers divides exactly by 3? (a) 5597 (b) 8820 (c) 2707 (d) 5509
  38. 38.How many factors does 49 have?
  39. 39.How many factors does 38 have?
  40. 40.How many factors does 28 have?

Answer key

  1. 2
  2. 3
  3. 10
  4. 4
  5. 6
  6. 4
  7. 10
  8. 3534
  9. 9888
  10. 2055
  11. 2
  12. 7527
  13. 8
  14. 4
  15. 2
  16. 6
  17. 3234
  18. 2
  19. 10
  20. 8
  21. 5
  22. 2
  23. 1
  24. 10
  25. 12
  26. 6411
  27. 6
  28. 9
  29. 1
  30. 6
  31. 8
  32. 8271
  33. 5
  34. 8
  35. 7
  36. 2144
  37. 8820
  38. 3
  39. 4
  40. 6

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