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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 120 · 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 3? (a) 7514 (b) 8043 (c) 3481 (d) 6316
  2. 2.What is the smallest number you must add to 689 so that it divides exactly by 11?
  3. 3.Which of these numbers divides exactly by 4? (a) 6125 (b) 3323 (c) 9996 (d) 6682
  4. 4.What is the smallest number you must add to 349 so that it divides exactly by 11?
  5. 5.What is the smallest number you must add to 595 so that it divides exactly by 6?
  6. 6.What is the smallest number you must add to 194 so that it divides exactly by 6?
  7. 7.How many factors does 45 have?
  8. 8.How many factors does 17 have?
  9. 9.What is the smallest number you must take away from 103 so that it divides exactly by 7?
  10. 10.Which of these numbers divides exactly by 8? (a) 1071 (b) 7120 (c) 5773 (d) 2844
  11. 11.What is the smallest number you must take away from 488 so that it divides exactly by 6?
  12. 12.Which of these numbers divides exactly by 4? (a) 9414 (b) 6666 (c) 1493 (d) 8856
  13. 13.What is the smallest number you must add to 783 so that it divides exactly by 7?
  14. 14.What is the smallest number you must add to 891 so that it divides exactly by 13?
  15. 15.How many factors does 34 have?
  16. 16.What is the smallest number you must add to 254 so that it divides exactly by 7?
  17. 17.What is the smallest number you must add to 683 so that it divides exactly by 12?
  18. 18.What is the smallest number you must take away from 873 so that it divides exactly by 4?
  19. 19.What is the smallest number you must add to 270 so that it divides exactly by 8?
  20. 20.How many factors does 77 have?
  21. 21.What is the smallest number you must add to 328 so that it divides exactly by 6?
  22. 22.How many factors does 72 have?
  23. 23.Which of these numbers divides exactly by 11? (a) 9083 (b) 1433 (c) 6924 (d) 4763
  24. 24.What is the smallest number you must add to 384 so that it divides exactly by 13?
  25. 25.Which of these numbers divides exactly by 8? (a) 1849 (b) 5183 (c) 3484 (d) 7912
  26. 26.How many factors does 97 have?
  27. 27.Which of these numbers divides exactly by 9? (a) 6339 (b) 2624 (c) 8631 (d) 5232
  28. 28.How many factors does 44 have?
  29. 29.How many factors does 38 have?
  30. 30.Which of these numbers divides exactly by 3? (a) 9136 (b) 7474 (c) 8608 (d) 6210
  31. 31.How many factors does 91 have?
  32. 32.What is the smallest number you must add to 896 so that it divides exactly by 11?
  33. 33.How many factors does 64 have?
  34. 34.What is the smallest number you must take away from 415 so that it divides exactly by 9?
  35. 35.How many factors does 32 have?
  36. 36.What is the smallest number you must take away from 570 so that it divides exactly by 12?
  37. 37.How many factors does 49 have?
  38. 38.How many factors does 29 have?
  39. 39.What is the smallest number you must take away from 191 so that it divides exactly by 6?
  40. 40.How many factors does 88 have?

Answer key

  1. 8043
  2. 4
  3. 9996
  4. 3
  5. 5
  6. 4
  7. 6
  8. 2
  9. 5
  10. 7120
  11. 2
  12. 8856
  13. 1
  14. 6
  15. 4
  16. 5
  17. 1
  18. 1
  19. 2
  20. 4
  21. 2
  22. 12
  23. 4763
  24. 6
  25. 7912
  26. 2
  27. 8631
  28. 6
  29. 4
  30. 6210
  31. 4
  32. 6
  33. 7
  34. 1
  35. 6
  36. 6
  37. 3
  38. 2
  39. 5
  40. 8

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