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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 180 · 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 99 have?
  2. 2.Which of these numbers divides exactly by 8? (a) 9288 (b) 2363 (c) 3810 (d) 6314
  3. 3.Which of these numbers divides exactly by 8? (a) 5344 (b) 4875 (c) 6748 (d) 3849
  4. 4.How many factors does 33 have?
  5. 5.How many factors does 51 have?
  6. 6.How many factors does 29 have?
  7. 7.What is the smallest number you must take away from 661 so that it divides exactly by 7?
  8. 8.How many factors does 19 have?
  9. 9.What is the smallest number you must add to 401 so that it divides exactly by 9?
  10. 10.What is the smallest number you must take away from 905 so that it divides exactly by 7?
  11. 11.How many factors does 68 have?
  12. 12.What is the smallest number you must add to 939 so that it divides exactly by 6?
  13. 13.How many factors does 47 have?
  14. 14.What is the smallest number you must take away from 229 so that it divides exactly by 13?
  15. 15.What is the smallest number you must take away from 276 so that it divides exactly by 8?
  16. 16.What is the smallest number you must add to 723 so that it divides exactly by 12?
  17. 17.Which of these numbers divides exactly by 8? (a) 2423 (b) 9888 (c) 4502 (d) 2644
  18. 18.What is the smallest number you must take away from 610 so that it divides exactly by 13?
  19. 19.What is the smallest number you must add to 971 so that it divides exactly by 6?
  20. 20.What is the smallest number you must add to 375 so that it divides exactly by 7?
  21. 21.What is the smallest number you must add to 335 so that it divides exactly by 7?
  22. 22.What is the smallest number you must take away from 143 so that it divides exactly by 6?
  23. 23.How many factors does 90 have?
  24. 24.Which of these numbers divides exactly by 9? (a) 1216 (b) 3204 (c) 3845 (d) 9192
  25. 25.What is the smallest number you must take away from 773 so that it divides exactly by 8?
  26. 26.Which of these numbers divides exactly by 3? (a) 4070 (b) 2553 (c) 5021 (d) 6749
  27. 27.What is the smallest number you must take away from 513 so that it divides exactly by 12?
  28. 28.How many factors does 26 have?
  29. 29.How many factors does 31 have?
  30. 30.Which of these numbers divides exactly by 3? (a) 8356 (b) 2584 (c) 8507 (d) 2121
  31. 31.How many factors does 70 have?
  32. 32.Which of these numbers divides exactly by 8? (a) 2114 (b) 1428 (c) 4292 (d) 7968
  33. 33.What is the smallest number you must take away from 456 so that it divides exactly by 13?
  34. 34.How many factors does 86 have?
  35. 35.What is the smallest number you must add to 708 so that it divides exactly by 7?
  36. 36.How many factors does 35 have?
  37. 37.What is the smallest number you must take away from 983 so that it divides exactly by 6?
  38. 38.What is the smallest number you must take away from 332 so that it divides exactly by 3?
  39. 39.What is the smallest number you must take away from 991 so that it divides exactly by 6?
  40. 40.How many factors does 41 have?

Answer key

  1. 6
  2. 9288
  3. 5344
  4. 4
  5. 4
  6. 2
  7. 3
  8. 2
  9. 4
  10. 2
  11. 6
  12. 3
  13. 2
  14. 8
  15. 4
  16. 9
  17. 9888
  18. 12
  19. 1
  20. 3
  21. 1
  22. 5
  23. 12
  24. 3204
  25. 5
  26. 2553
  27. 9
  28. 4
  29. 2
  30. 2121
  31. 8
  32. 7968
  33. 1
  34. 4
  35. 6
  36. 4
  37. 5
  38. 2
  39. 1
  40. 2

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