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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 137 · 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.Which of these numbers divides exactly by 8? (a) 4999 (b) 3192 (c) 6889 (d) 3479
  2. 2.How many factors does 14 have?
  3. 3.What is the smallest number you must add to 521 so that it divides exactly by 12?
  4. 4.What is the smallest number you must add to 726 so that it divides exactly by 9?
  5. 5.What is the smallest number you must take away from 759 so that it divides exactly by 13?
  6. 6.What is the smallest number you must add to 731 so that it divides exactly by 8?
  7. 7.What is the smallest number you must add to 316 so that it divides exactly by 8?
  8. 8.How many factors does 29 have?
  9. 9.Which of these numbers divides exactly by 3? (a) 9890 (b) 3422 (c) 8880 (d) 1141
  10. 10.How many factors does 37 have?
  11. 11.What is the smallest number you must add to 471 so that it divides exactly by 12?
  12. 12.What is the smallest number you must add to 271 so that it divides exactly by 6?
  13. 13.What is the smallest number you must add to 414 so that it divides exactly by 12?
  14. 14.Which of these numbers divides exactly by 9? (a) 7928 (b) 4604 (c) 7308 (d) 8099
  15. 15.How many factors does 15 have?
  16. 16.What is the smallest number you must take away from 297 so that it divides exactly by 13?
  17. 17.What is the smallest number you must take away from 302 so that it divides exactly by 13?
  18. 18.What is the smallest number you must take away from 386 so that it divides exactly by 7?
  19. 19.What is the smallest number you must add to 561 so that it divides exactly by 8?
  20. 20.What is the smallest number you must add to 705 so that it divides exactly by 7?
  21. 21.What is the smallest number you must take away from 601 so that it divides exactly by 11?
  22. 22.How many factors does 41 have?
  23. 23.How many factors does 79 have?
  24. 24.Which of these numbers divides exactly by 4? (a) 3996 (b) 3411 (c) 9159 (d) 6033
  25. 25.How many factors does 47 have?
  26. 26.How many factors does 38 have?
  27. 27.What is the smallest number you must add to 374 so that it divides exactly by 4?
  28. 28.What is the smallest number you must take away from 501 so that it divides exactly by 8?
  29. 29.Which of these numbers divides exactly by 3? (a) 9715 (b) 4609 (c) 3132 (d) 1066
  30. 30.How many factors does 42 have?
  31. 31.What is the smallest number you must take away from 410 so that it divides exactly by 7?
  32. 32.What is the smallest number you must take away from 990 so that it divides exactly by 8?
  33. 33.Which of these numbers divides exactly by 3? (a) 5396 (b) 6114 (c) 5263 (d) 7406
  34. 34.What is the smallest number you must take away from 151 so that it divides exactly by 11?
  35. 35.Which of these numbers divides exactly by 6? (a) 6061 (b) 7686 (c) 8573 (d) 4151
  36. 36.Which of these numbers divides exactly by 9? (a) 6565 (b) 2857 (c) 2220 (d) 1107
  37. 37.What is the smallest number you must add to 841 so that it divides exactly by 9?
  38. 38.How many factors does 61 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 7417 (b) 2834 (c) 6278 (d) 3099
  40. 40.What is the smallest number you must take away from 548 so that it divides exactly by 6?

Answer key

  1. 3192
  2. 4
  3. 7
  4. 3
  5. 5
  6. 5
  7. 4
  8. 2
  9. 8880
  10. 2
  11. 9
  12. 5
  13. 6
  14. 7308
  15. 4
  16. 11
  17. 3
  18. 1
  19. 7
  20. 2
  21. 7
  22. 2
  23. 2
  24. 3996
  25. 2
  26. 4
  27. 2
  28. 5
  29. 3132
  30. 8
  31. 4
  32. 6
  33. 6114
  34. 8
  35. 7686
  36. 1107
  37. 5
  38. 2
  39. 3099
  40. 2

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