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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 213 · 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 251 so that it divides exactly by 6?
  2. 2.Which of these numbers divides exactly by 11? (a) 1019 (b) 3059 (c) 1969 (d) 3054
  3. 3.How many factors does 41 have?
  4. 4.Which of these numbers divides exactly by 11? (a) 8085 (b) 9480 (c) 9775 (d) 4985
  5. 5.How many factors does 62 have?
  6. 6.How many factors does 71 have?
  7. 7.Which of these numbers divides exactly by 9? (a) 1757 (b) 2057 (c) 7820 (d) 9117
  8. 8.Which of these numbers divides exactly by 6? (a) 6154 (b) 6847 (c) 8524 (d) 5166
  9. 9.What is the smallest number you must add to 515 so that it divides exactly by 13?
  10. 10.What is the smallest number you must add to 702 so that it divides exactly by 12?
  11. 11.What is the smallest number you must take away from 318 so that it divides exactly by 12?
  12. 12.What is the smallest number you must take away from 674 so that it divides exactly by 3?
  13. 13.What is the smallest number you must add to 741 so that it divides exactly by 8?
  14. 14.How many factors does 12 have?
  15. 15.Which of these numbers divides exactly by 6? (a) 9781 (b) 3166 (c) 4945 (d) 1884
  16. 16.What is the smallest number you must add to 291 so that it divides exactly by 11?
  17. 17.How many factors does 49 have?
  18. 18.How many factors does 37 have?
  19. 19.How many factors does 98 have?
  20. 20.What is the smallest number you must add to 146 so that it divides exactly by 11?
  21. 21.How many factors does 66 have?
  22. 22.What is the smallest number you must add to 797 so that it divides exactly by 9?
  23. 23.How many factors does 34 have?
  24. 24.What is the smallest number you must add to 893 so that it divides exactly by 6?
  25. 25.Which of these numbers divides exactly by 11? (a) 8463 (b) 4631 (c) 5869 (d) 8882
  26. 26.Which of these numbers divides exactly by 3? (a) 9695 (b) 9697 (c) 9471 (d) 6278
  27. 27.What is the smallest number you must take away from 290 so that it divides exactly by 7?
  28. 28.How many factors does 55 have?
  29. 29.What is the smallest number you must take away from 631 so that it divides exactly by 6?
  30. 30.What is the smallest number you must take away from 198 so that it divides exactly by 12?
  31. 31.How many factors does 89 have?
  32. 32.How many factors does 24 have?
  33. 33.What is the smallest number you must add to 654 so that it divides exactly by 11?
  34. 34.Which of these numbers divides exactly by 3? (a) 7860 (b) 6308 (c) 6523 (d) 3022
  35. 35.Which of these numbers divides exactly by 4? (a) 1809 (b) 9813 (c) 4424 (d) 3637
  36. 36.What is the smallest number you must add to 110 so that it divides exactly by 3?
  37. 37.How many factors does 52 have?
  38. 38.How many factors does 47 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 5454 (b) 9775 (c) 5717 (d) 1184
  40. 40.How many factors does 58 have?

Answer key

  1. 1
  2. 1969
  3. 2
  4. 8085
  5. 4
  6. 2
  7. 9117
  8. 5166
  9. 5
  10. 6
  11. 6
  12. 2
  13. 3
  14. 6
  15. 1884
  16. 6
  17. 3
  18. 2
  19. 6
  20. 8
  21. 8
  22. 4
  23. 4
  24. 1
  25. 4631
  26. 9471
  27. 3
  28. 4
  29. 1
  30. 6
  31. 2
  32. 8
  33. 6
  34. 7860
  35. 4424
  36. 1
  37. 6
  38. 2
  39. 5454
  40. 4

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