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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 98 · 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 642 so that it divides exactly by 8?
  2. 2.What is the smallest number you must add to 189 so that it divides exactly by 13?
  3. 3.How many factors does 33 have?
  4. 4.What is the smallest number you must take away from 381 so that it divides exactly by 9?
  5. 5.How many factors does 90 have?
  6. 6.Which of these numbers divides exactly by 8? (a) 3079 (b) 7442 (c) 5349 (d) 9256
  7. 7.What is the smallest number you must add to 211 so that it divides exactly by 4?
  8. 8.What is the smallest number you must take away from 537 so that it divides exactly by 8?
  9. 9.What is the smallest number you must take away from 855 so that it divides exactly by 8?
  10. 10.How many factors does 49 have?
  11. 11.What is the smallest number you must add to 432 so that it divides exactly by 7?
  12. 12.Which of these numbers divides exactly by 3? (a) 6652 (b) 3335 (c) 2222 (d) 4779
  13. 13.How many factors does 80 have?
  14. 14.What is the smallest number you must add to 902 so that it divides exactly by 8?
  15. 15.What is the smallest number you must add to 509 so that it divides exactly by 3?
  16. 16.What is the smallest number you must take away from 667 so that it divides exactly by 3?
  17. 17.Which of these numbers divides exactly by 4? (a) 9750 (b) 5194 (c) 7632 (d) 5766
  18. 18.What is the smallest number you must add to 811 so that it divides exactly by 8?
  19. 19.How many factors does 32 have?
  20. 20.What is the smallest number you must add to 279 so that it divides exactly by 7?
  21. 21.How many factors does 21 have?
  22. 22.What is the smallest number you must add to 926 so that it divides exactly by 7?
  23. 23.How many factors does 75 have?
  24. 24.How many factors does 20 have?
  25. 25.How many factors does 42 have?
  26. 26.What is the smallest number you must add to 673 so that it divides exactly by 11?
  27. 27.Which of these numbers divides exactly by 6? (a) 5993 (b) 1765 (c) 2154 (d) 6322
  28. 28.What is the smallest number you must add to 646 so that it divides exactly by 6?
  29. 29.Which of these numbers divides exactly by 3? (a) 5505 (b) 7118 (c) 5038 (d) 7843
  30. 30.Which of these numbers divides exactly by 4? (a) 1154 (b) 2649 (c) 9316 (d) 3663
  31. 31.How many factors does 26 have?
  32. 32.What is the smallest number you must add to 371 so that it divides exactly by 13?
  33. 33.How many factors does 44 have?
  34. 34.What is the smallest number you must add to 452 so that it divides exactly by 8?
  35. 35.How many factors does 86 have?
  36. 36.What is the smallest number you must take away from 279 so that it divides exactly by 7?
  37. 37.What is the smallest number you must take away from 705 so that it divides exactly by 4?
  38. 38.What is the smallest number you must take away from 551 so that it divides exactly by 12?
  39. 39.Which of these numbers divides exactly by 6? (a) 5841 (b) 3749 (c) 7218 (d) 2607
  40. 40.Which of these numbers divides exactly by 6? (a) 8286 (b) 8433 (c) 2569 (d) 9921

Answer key

  1. 2
  2. 6
  3. 4
  4. 3
  5. 12
  6. 9256
  7. 1
  8. 1
  9. 7
  10. 3
  11. 2
  12. 4779
  13. 10
  14. 2
  15. 1
  16. 1
  17. 7632
  18. 5
  19. 6
  20. 1
  21. 4
  22. 5
  23. 6
  24. 6
  25. 8
  26. 9
  27. 2154
  28. 2
  29. 5505
  30. 9316
  31. 4
  32. 6
  33. 6
  34. 4
  35. 4
  36. 6
  37. 1
  38. 11
  39. 7218
  40. 8286

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