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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 230 · 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 take away from 576 so that it divides exactly by 7?
  2. 2.Which of these numbers divides exactly by 3? (a) 7903 (b) 8582 (c) 2382 (d) 2222
  3. 3.What is the smallest number you must take away from 733 so that it divides exactly by 7?
  4. 4.How many factors does 99 have?
  5. 5.What is the smallest number you must take away from 634 so that it divides exactly by 12?
  6. 6.How many factors does 33 have?
  7. 7.What is the smallest number you must add to 283 so that it divides exactly by 12?
  8. 8.How many factors does 77 have?
  9. 9.How many factors does 48 have?
  10. 10.How many factors does 72 have?
  11. 11.How many factors does 40 have?
  12. 12.How many factors does 56 have?
  13. 13.How many factors does 73 have?
  14. 14.How many factors does 55 have?
  15. 15.How many factors does 75 have?
  16. 16.How many factors does 35 have?
  17. 17.What is the smallest number you must take away from 463 so that it divides exactly by 8?
  18. 18.Which of these numbers divides exactly by 11? (a) 1329 (b) 5263 (c) 9369 (d) 9009
  19. 19.What is the smallest number you must take away from 531 so that it divides exactly by 12?
  20. 20.Which of these numbers divides exactly by 4? (a) 6370 (b) 2038 (c) 1964 (d) 7850
  21. 21.How many factors does 79 have?
  22. 22.What is the smallest number you must add to 458 so that it divides exactly by 12?
  23. 23.What is the smallest number you must take away from 419 so that it divides exactly by 12?
  24. 24.Which of these numbers divides exactly by 6? (a) 2158 (b) 3040 (c) 4314 (d) 1445
  25. 25.Which of these numbers divides exactly by 11? (a) 9139 (b) 6936 (c) 3333 (d) 6834
  26. 26.How many factors does 51 have?
  27. 27.What is the smallest number you must take away from 791 so that it divides exactly by 6?
  28. 28.How many factors does 47 have?
  29. 29.Which of these numbers divides exactly by 4? (a) 8785 (b) 7279 (c) 7249 (d) 2524
  30. 30.What is the smallest number you must add to 275 so that it divides exactly by 9?
  31. 31.Which of these numbers divides exactly by 9? (a) 5912 (b) 8446 (c) 1503 (d) 2869
  32. 32.Which of these numbers divides exactly by 3? (a) 9954 (b) 1913 (c) 9086 (d) 1384
  33. 33.How many factors does 37 have?
  34. 34.What is the smallest number you must take away from 987 so that it divides exactly by 6?
  35. 35.Which of these numbers divides exactly by 8? (a) 1204 (b) 5243 (c) 3200 (d) 8930
  36. 36.What is the smallest number you must take away from 432 so that it divides exactly by 7?
  37. 37.How many factors does 31 have?
  38. 38.What is the smallest number you must add to 602 so that it divides exactly by 11?
  39. 39.What is the smallest number you must add to 683 so that it divides exactly by 11?
  40. 40.What is the smallest number you must take away from 551 so that it divides exactly by 13?

Answer key

  1. 2
  2. 2382
  3. 5
  4. 6
  5. 10
  6. 4
  7. 5
  8. 4
  9. 10
  10. 12
  11. 8
  12. 8
  13. 2
  14. 4
  15. 6
  16. 4
  17. 7
  18. 9009
  19. 3
  20. 1964
  21. 2
  22. 10
  23. 11
  24. 4314
  25. 3333
  26. 4
  27. 5
  28. 2
  29. 2524
  30. 4
  31. 1503
  32. 9954
  33. 2
  34. 3
  35. 3200
  36. 5
  37. 2
  38. 3
  39. 10
  40. 5

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