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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 165 · 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 858 so that it divides exactly by 7?
  2. 2.Which of these numbers divides exactly by 8? (a) 3268 (b) 1429 (c) 2808 (d) 9914
  3. 3.What is the smallest number you must take away from 236 so that it divides exactly by 6?
  4. 4.What is the smallest number you must take away from 443 so that it divides exactly by 13?
  5. 5.What is the smallest number you must add to 610 so that it divides exactly by 6?
  6. 6.How many factors does 25 have?
  7. 7.How many factors does 46 have?
  8. 8.How many factors does 39 have?
  9. 9.How many factors does 34 have?
  10. 10.Which of these numbers divides exactly by 11? (a) 3921 (b) 6363 (c) 3707 (d) 2881
  11. 11.Which of these numbers divides exactly by 9? (a) 8764 (b) 8537 (c) 7337 (d) 4401
  12. 12.How many factors does 92 have?
  13. 13.Which of these numbers divides exactly by 4? (a) 6248 (b) 4758 (c) 2939 (d) 3945
  14. 14.Which of these numbers divides exactly by 8? (a) 9971 (b) 1880 (c) 3827 (d) 1276
  15. 15.Which of these numbers divides exactly by 11? (a) 1838 (b) 3542 (c) 6830 (d) 4354
  16. 16.What is the smallest number you must take away from 255 so that it divides exactly by 12?
  17. 17.Which of these numbers divides exactly by 6? (a) 1875 (b) 8666 (c) 7092 (d) 4480
  18. 18.What is the smallest number you must take away from 633 so that it divides exactly by 11?
  19. 19.What is the smallest number you must add to 343 so that it divides exactly by 4?
  20. 20.How many factors does 42 have?
  21. 21.How many factors does 24 have?
  22. 22.How many factors does 47 have?
  23. 23.What is the smallest number you must add to 601 so that it divides exactly by 4?
  24. 24.What is the smallest number you must add to 269 so that it divides exactly by 12?
  25. 25.How many factors does 23 have?
  26. 26.What is the smallest number you must take away from 237 so that it divides exactly by 11?
  27. 27.What is the smallest number you must add to 937 so that it divides exactly by 13?
  28. 28.What is the smallest number you must add to 181 so that it divides exactly by 3?
  29. 29.Which of these numbers divides exactly by 4? (a) 3746 (b) 7566 (c) 2734 (d) 4268
  30. 30.What is the smallest number you must take away from 129 so that it divides exactly by 13?
  31. 31.What is the smallest number you must add to 158 so that it divides exactly by 11?
  32. 32.How many factors does 84 have?
  33. 33.How many factors does 97 have?
  34. 34.How many factors does 89 have?
  35. 35.What is the smallest number you must take away from 656 so that it divides exactly by 13?
  36. 36.What is the smallest number you must add to 915 so that it divides exactly by 8?
  37. 37.How many factors does 20 have?
  38. 38.Which of these numbers divides exactly by 8? (a) 2624 (b) 8929 (c) 7884 (d) 1939
  39. 39.How many factors does 51 have?
  40. 40.How many factors does 52 have?

Answer key

  1. 3
  2. 2808
  3. 2
  4. 1
  5. 2
  6. 3
  7. 4
  8. 4
  9. 4
  10. 3707
  11. 4401
  12. 6
  13. 6248
  14. 1880
  15. 3542
  16. 3
  17. 7092
  18. 6
  19. 1
  20. 8
  21. 8
  22. 2
  23. 3
  24. 7
  25. 2
  26. 6
  27. 12
  28. 2
  29. 4268
  30. 12
  31. 7
  32. 12
  33. 2
  34. 2
  35. 6
  36. 5
  37. 6
  38. 2624
  39. 4
  40. 6

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