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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 241 · 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 488 so that it divides exactly by 9?
  2. 2.Which of these numbers divides exactly by 4? (a) 6362 (b) 4473 (c) 8527 (d) 7204
  3. 3.How many factors does 24 have?
  4. 4.How many factors does 34 have?
  5. 5.How many factors does 32 have?
  6. 6.Which of these numbers divides exactly by 6? (a) 6719 (b) 1892 (c) 5824 (d) 3054
  7. 7.What is the smallest number you must take away from 243 so that it divides exactly by 8?
  8. 8.Which of these numbers divides exactly by 4? (a) 2788 (b) 2574 (c) 3557 (d) 4215
  9. 9.How many factors does 80 have?
  10. 10.Which of these numbers divides exactly by 9? (a) 3215 (b) 1002 (c) 9198 (d) 8381
  11. 11.How many factors does 37 have?
  12. 12.What is the smallest number you must add to 884 so that it divides exactly by 7?
  13. 13.How many factors does 56 have?
  14. 14.What is the smallest number you must add to 204 so that it divides exactly by 11?
  15. 15.What is the smallest number you must take away from 959 so that it divides exactly by 13?
  16. 16.What is the smallest number you must add to 351 so that it divides exactly by 4?
  17. 17.What is the smallest number you must take away from 249 so that it divides exactly by 8?
  18. 18.How many factors does 46 have?
  19. 19.Which of these numbers divides exactly by 4? (a) 7553 (b) 8962 (c) 5218 (d) 8380
  20. 20.How many factors does 89 have?
  21. 21.How many factors does 58 have?
  22. 22.What is the smallest number you must take away from 771 so that it divides exactly by 4?
  23. 23.Which of these numbers divides exactly by 6? (a) 7805 (b) 4584 (c) 7919 (d) 6637
  24. 24.What is the smallest number you must take away from 870 so that it divides exactly by 4?
  25. 25.How many factors does 59 have?
  26. 26.What is the smallest number you must take away from 437 so that it divides exactly by 11?
  27. 27.What is the smallest number you must take away from 141 so that it divides exactly by 9?
  28. 28.How many factors does 55 have?
  29. 29.How many factors does 65 have?
  30. 30.How many factors does 31 have?
  31. 31.How many factors does 61 have?
  32. 32.Which of these numbers divides exactly by 8? (a) 7310 (b) 6434 (c) 2142 (d) 6480
  33. 33.What is the smallest number you must add to 658 so that it divides exactly by 4?
  34. 34.What is the smallest number you must add to 620 so that it divides exactly by 6?
  35. 35.What is the smallest number you must take away from 969 so that it divides exactly by 11?
  36. 36.Which of these numbers divides exactly by 3? (a) 2842 (b) 2660 (c) 3380 (d) 6972
  37. 37.What is the smallest number you must take away from 517 so that it divides exactly by 4?
  38. 38.Which of these numbers divides exactly by 6? (a) 9754 (b) 7884 (c) 3488 (d) 2159
  39. 39.What is the smallest number you must take away from 868 so that it divides exactly by 12?
  40. 40.What is the smallest number you must add to 496 so that it divides exactly by 9?

Answer key

  1. 7
  2. 7204
  3. 8
  4. 4
  5. 6
  6. 3054
  7. 3
  8. 2788
  9. 10
  10. 9198
  11. 2
  12. 5
  13. 8
  14. 5
  15. 10
  16. 1
  17. 1
  18. 4
  19. 8380
  20. 2
  21. 4
  22. 3
  23. 4584
  24. 2
  25. 2
  26. 8
  27. 6
  28. 4
  29. 4
  30. 2
  31. 2
  32. 6480
  33. 2
  34. 4
  35. 1
  36. 6972
  37. 1
  38. 7884
  39. 4
  40. 8

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