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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 58 · 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 911 so that it divides exactly by 12?
  2. 2.What is the smallest number you must take away from 508 so that it divides exactly by 3?
  3. 3.What is the smallest number you must take away from 717 so that it divides exactly by 9?
  4. 4.What is the smallest number you must take away from 365 so that it divides exactly by 9?
  5. 5.Which of these numbers divides exactly by 3? (a) 9474 (b) 4727 (c) 4480 (d) 8968
  6. 6.How many factors does 34 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 9951 (b) 5695 (c) 5885 (d) 1222
  8. 8.What is the smallest number you must add to 980 so that it divides exactly by 11?
  9. 9.What is the smallest number you must add to 509 so that it divides exactly by 11?
  10. 10.What is the smallest number you must add to 466 so that it divides exactly by 9?
  11. 11.What is the smallest number you must add to 105 so that it divides exactly by 6?
  12. 12.What is the smallest number you must take away from 126 so that it divides exactly by 11?
  13. 13.What is the smallest number you must add to 403 so that it divides exactly by 8?
  14. 14.What is the smallest number you must take away from 254 so that it divides exactly by 6?
  15. 15.What is the smallest number you must add to 309 so that it divides exactly by 4?
  16. 16.What is the smallest number you must add to 572 so that it divides exactly by 6?
  17. 17.What is the smallest number you must add to 962 so that it divides exactly by 3?
  18. 18.What is the smallest number you must add to 939 so that it divides exactly by 7?
  19. 19.What is the smallest number you must add to 201 so that it divides exactly by 7?
  20. 20.Which of these numbers divides exactly by 8? (a) 6857 (b) 3360 (c) 8949 (d) 3257
  21. 21.How many factors does 43 have?
  22. 22.What is the smallest number you must take away from 757 so that it divides exactly by 7?
  23. 23.What is the smallest number you must take away from 747 so that it divides exactly by 13?
  24. 24.How many factors does 27 have?
  25. 25.How many factors does 87 have?
  26. 26.How many factors does 28 have?
  27. 27.What is the smallest number you must take away from 464 so that it divides exactly by 6?
  28. 28.What is the smallest number you must take away from 813 so that it divides exactly by 7?
  29. 29.Which of these numbers divides exactly by 9? (a) 1368 (b) 1508 (c) 8954 (d) 4790
  30. 30.Which of these numbers divides exactly by 11? (a) 7964 (b) 5326 (c) 5922 (d) 6166
  31. 31.How many factors does 82 have?
  32. 32.What is the smallest number you must take away from 357 so that it divides exactly by 9?
  33. 33.What is the smallest number you must take away from 686 so that it divides exactly by 3?
  34. 34.What is the smallest number you must add to 469 so that it divides exactly by 9?
  35. 35.What is the smallest number you must take away from 187 so that it divides exactly by 3?
  36. 36.Which of these numbers divides exactly by 11? (a) 7323 (b) 1582 (c) 6545 (d) 6599
  37. 37.Which of these numbers divides exactly by 3? (a) 2804 (b) 5233 (c) 5487 (d) 5780
  38. 38.What is the smallest number you must add to 211 so that it divides exactly by 9?
  39. 39.How many factors does 22 have?
  40. 40.Which of these numbers divides exactly by 9? (a) 5463 (b) 9839 (c) 9732 (d) 9346

Answer key

  1. 11
  2. 1
  3. 6
  4. 5
  5. 9474
  6. 4
  7. 5885
  8. 10
  9. 8
  10. 2
  11. 3
  12. 5
  13. 5
  14. 2
  15. 3
  16. 4
  17. 1
  18. 6
  19. 2
  20. 3360
  21. 2
  22. 1
  23. 6
  24. 4
  25. 4
  26. 6
  27. 2
  28. 1
  29. 1368
  30. 7964
  31. 4
  32. 6
  33. 2
  34. 8
  35. 1
  36. 6545
  37. 5487
  38. 5
  39. 4
  40. 5463

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