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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 224 · 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.Which of these numbers divides exactly by 11? (a) 8074 (b) 7889 (c) 3687 (d) 2867
  2. 2.How many factors does 19 have?
  3. 3.Which of these numbers divides exactly by 9? (a) 7568 (b) 9594 (c) 2908 (d) 7086
  4. 4.What is the smallest number you must add to 835 so that it divides exactly by 6?
  5. 5.What is the smallest number you must take away from 690 so that it divides exactly by 9?
  6. 6.How many factors does 51 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 1750 (b) 5287 (c) 5280 (d) 1368
  8. 8.What is the smallest number you must take away from 619 so that it divides exactly by 3?
  9. 9.What is the smallest number you must take away from 116 so that it divides exactly by 7?
  10. 10.What is the smallest number you must add to 599 so that it divides exactly by 6?
  11. 11.What is the smallest number you must add to 887 so that it divides exactly by 6?
  12. 12.What is the smallest number you must add to 197 so that it divides exactly by 12?
  13. 13.What is the smallest number you must add to 519 so that it divides exactly by 13?
  14. 14.How many factors does 64 have?
  15. 15.What is the smallest number you must take away from 916 so that it divides exactly by 8?
  16. 16.Which of these numbers divides exactly by 6? (a) 9481 (b) 3659 (c) 5399 (d) 3984
  17. 17.Which of these numbers divides exactly by 11? (a) 7777 (b) 7175 (c) 2740 (d) 2264
  18. 18.What is the smallest number you must add to 564 so that it divides exactly by 7?
  19. 19.How many factors does 15 have?
  20. 20.Which of these numbers divides exactly by 3? (a) 9588 (b) 9136 (c) 3595 (d) 3470
  21. 21.What is the smallest number you must take away from 249 so that it divides exactly by 9?
  22. 22.How many factors does 37 have?
  23. 23.Which of these numbers divides exactly by 3? (a) 9378 (b) 7066 (c) 5734 (d) 4318
  24. 24.How many factors does 54 have?
  25. 25.Which of these numbers divides exactly by 4? (a) 2607 (b) 7640 (c) 3253 (d) 2318
  26. 26.How many factors does 16 have?
  27. 27.How many factors does 48 have?
  28. 28.What is the smallest number you must add to 947 so that it divides exactly by 3?
  29. 29.How many factors does 73 have?
  30. 30.What is the smallest number you must add to 865 so that it divides exactly by 6?
  31. 31.How many factors does 91 have?
  32. 32.How many factors does 14 have?
  33. 33.What is the smallest number you must add to 330 so that it divides exactly by 7?
  34. 34.What is the smallest number you must add to 667 so that it divides exactly by 7?
  35. 35.How many factors does 56 have?
  36. 36.How many factors does 71 have?
  37. 37.How many factors does 21 have?
  38. 38.Which of these numbers divides exactly by 3? (a) 4252 (b) 7687 (c) 6561 (d) 6928
  39. 39.Which of these numbers divides exactly by 4? (a) 3220 (b) 1783 (c) 2483 (d) 9483
  40. 40.Which of these numbers divides exactly by 8? (a) 1938 (b) 9307 (c) 9055 (d) 6872

Answer key

  1. 8074
  2. 2
  3. 9594
  4. 5
  5. 6
  6. 4
  7. 5280
  8. 1
  9. 4
  10. 1
  11. 1
  12. 7
  13. 1
  14. 7
  15. 4
  16. 3984
  17. 7777
  18. 3
  19. 4
  20. 9588
  21. 6
  22. 2
  23. 9378
  24. 8
  25. 7640
  26. 5
  27. 10
  28. 1
  29. 2
  30. 5
  31. 4
  32. 4
  33. 6
  34. 5
  35. 8
  36. 2
  37. 4
  38. 6561
  39. 3220
  40. 6872

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