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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 282 · 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 63 have?
  2. 2.How many factors does 79 have?
  3. 3.What is the smallest number you must add to 776 so that it divides exactly by 11?
  4. 4.What is the smallest number you must add to 988 so that it divides exactly by 6?
  5. 5.What is the smallest number you must take away from 375 so that it divides exactly by 6?
  6. 6.How many factors does 25 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 9005 (b) 6303 (c) 6518 (d) 2897
  8. 8.How many factors does 30 have?
  9. 9.What is the smallest number you must take away from 810 so that it divides exactly by 4?
  10. 10.Which of these numbers divides exactly by 3? (a) 2756 (b) 3359 (c) 9275 (d) 7782
  11. 11.How many factors does 65 have?
  12. 12.What is the smallest number you must take away from 380 so that it divides exactly by 3?
  13. 13.Which of these numbers divides exactly by 6? (a) 8008 (b) 6504 (c) 7186 (d) 7455
  14. 14.What is the smallest number you must take away from 517 so that it divides exactly by 8?
  15. 15.Which of these numbers divides exactly by 6? (a) 2501 (b) 6114 (c) 5831 (d) 6527
  16. 16.How many factors does 87 have?
  17. 17.What is the smallest number you must add to 917 so that it divides exactly by 13?
  18. 18.What is the smallest number you must add to 478 so that it divides exactly by 4?
  19. 19.Which of these numbers divides exactly by 3? (a) 5174 (b) 1535 (c) 4776 (d) 2753
  20. 20.Which of these numbers divides exactly by 4? (a) 2653 (b) 5349 (c) 2549 (d) 3528
  21. 21.Which of these numbers divides exactly by 4? (a) 1343 (b) 5562 (c) 4536 (d) 3015
  22. 22.What is the smallest number you must take away from 508 so that it divides exactly by 9?
  23. 23.How many factors does 21 have?
  24. 24.How many factors does 46 have?
  25. 25.Which of these numbers divides exactly by 3? (a) 2254 (b) 7329 (c) 6667 (d) 9691
  26. 26.What is the smallest number you must take away from 645 so that it divides exactly by 11?
  27. 27.How many factors does 16 have?
  28. 28.How many factors does 84 have?
  29. 29.What is the smallest number you must take away from 519 so that it divides exactly by 12?
  30. 30.How many factors does 27 have?
  31. 31.Which of these numbers divides exactly by 9? (a) 7029 (b) 3694 (c) 2960 (d) 7458
  32. 32.How many factors does 96 have?
  33. 33.How many factors does 93 have?
  34. 34.Which of these numbers divides exactly by 9? (a) 3232 (b) 8774 (c) 1881 (d) 2597
  35. 35.What is the smallest number you must add to 977 so that it divides exactly by 11?
  36. 36.How many factors does 98 have?
  37. 37.What is the smallest number you must take away from 269 so that it divides exactly by 7?
  38. 38.How many factors does 71 have?
  39. 39.What is the smallest number you must add to 207 so that it divides exactly by 8?
  40. 40.How many factors does 17 have?

Answer key

  1. 6
  2. 2
  3. 5
  4. 2
  5. 3
  6. 3
  7. 6303
  8. 8
  9. 2
  10. 7782
  11. 4
  12. 2
  13. 6504
  14. 5
  15. 6114
  16. 4
  17. 6
  18. 2
  19. 4776
  20. 3528
  21. 4536
  22. 4
  23. 4
  24. 4
  25. 7329
  26. 7
  27. 5
  28. 12
  29. 3
  30. 4
  31. 7029
  32. 12
  33. 4
  34. 1881
  35. 2
  36. 6
  37. 3
  38. 2
  39. 1
  40. 2

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