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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 226 · 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 405 so that it divides exactly by 11?
  2. 2.How many factors does 33 have?
  3. 3.How many factors does 12 have?
  4. 4.What is the smallest number you must add to 226 so that it divides exactly by 11?
  5. 5.Which of these numbers divides exactly by 9? (a) 4581 (b) 5344 (c) 3164 (d) 1562
  6. 6.What is the smallest number you must take away from 916 so that it divides exactly by 11?
  7. 7.What is the smallest number you must add to 220 so that it divides exactly by 12?
  8. 8.How many factors does 75 have?
  9. 9.What is the smallest number you must add to 123 so that it divides exactly by 8?
  10. 10.How many factors does 52 have?
  11. 11.What is the smallest number you must add to 337 so that it divides exactly by 8?
  12. 12.How many factors does 21 have?
  13. 13.What is the smallest number you must take away from 406 so that it divides exactly by 13?
  14. 14.Which of these numbers divides exactly by 3? (a) 2384 (b) 4787 (c) 8660 (d) 4032
  15. 15.How many factors does 70 have?
  16. 16.What is the smallest number you must take away from 466 so that it divides exactly by 13?
  17. 17.How many factors does 76 have?
  18. 18.How many factors does 26 have?
  19. 19.Which of these numbers divides exactly by 4? (a) 6686 (b) 7595 (c) 5843 (d) 4752
  20. 20.What is the smallest number you must take away from 941 so that it divides exactly by 9?
  21. 21.How many factors does 79 have?
  22. 22.What is the smallest number you must take away from 628 so that it divides exactly by 8?
  23. 23.What is the smallest number you must take away from 539 so that it divides exactly by 3?
  24. 24.Which of these numbers divides exactly by 3? (a) 8851 (b) 4116 (c) 3398 (d) 6290
  25. 25.How many factors does 62 have?
  26. 26.Which of these numbers divides exactly by 9? (a) 2861 (b) 7650 (c) 7111 (d) 7778
  27. 27.What is the smallest number you must take away from 885 so that it divides exactly by 9?
  28. 28.Which of these numbers divides exactly by 6? (a) 9015 (b) 7195 (c) 7202 (d) 6282
  29. 29.What is the smallest number you must take away from 695 so that it divides exactly by 4?
  30. 30.Which of these numbers divides exactly by 6? (a) 8745 (b) 4271 (c) 4510 (d) 3696
  31. 31.What is the smallest number you must add to 598 so that it divides exactly by 3?
  32. 32.What is the smallest number you must add to 208 so that it divides exactly by 12?
  33. 33.What is the smallest number you must add to 115 so that it divides exactly by 6?
  34. 34.How many factors does 54 have?
  35. 35.Which of these numbers divides exactly by 6? (a) 9023 (b) 5584 (c) 6612 (d) 3278
  36. 36.What is the smallest number you must take away from 567 so that it divides exactly by 6?
  37. 37.Which of these numbers divides exactly by 9? (a) 8451 (b) 1330 (c) 9580 (d) 8670
  38. 38.What is the smallest number you must add to 492 so that it divides exactly by 8?
  39. 39.How many factors does 29 have?
  40. 40.How many factors does 45 have?

Answer key

  1. 2
  2. 4
  3. 6
  4. 5
  5. 4581
  6. 3
  7. 8
  8. 6
  9. 5
  10. 6
  11. 7
  12. 4
  13. 3
  14. 4032
  15. 8
  16. 11
  17. 6
  18. 4
  19. 4752
  20. 5
  21. 2
  22. 4
  23. 2
  24. 4116
  25. 4
  26. 7650
  27. 3
  28. 6282
  29. 3
  30. 3696
  31. 2
  32. 8
  33. 5
  34. 8
  35. 6612
  36. 3
  37. 8451
  38. 4
  39. 2
  40. 6

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