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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 32 · 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.How many factors does 84 have?
  2. 2.What is the smallest number you must take away from 211 so that it divides exactly by 4?
  3. 3.How many factors does 63 have?
  4. 4.How many factors does 83 have?
  5. 5.What is the smallest number you must take away from 239 so that it divides exactly by 12?
  6. 6.What is the smallest number you must take away from 352 so that it divides exactly by 6?
  7. 7.Which of these numbers divides exactly by 11? (a) 6094 (b) 7507 (c) 7485 (d) 2217
  8. 8.How many factors does 15 have?
  9. 9.What is the smallest number you must add to 196 so that it divides exactly by 11?
  10. 10.How many factors does 86 have?
  11. 11.What is the smallest number you must take away from 437 so that it divides exactly by 3?
  12. 12.Which of these numbers divides exactly by 9? (a) 7778 (b) 4622 (c) 6838 (d) 7434
  13. 13.What is the smallest number you must take away from 955 so that it divides exactly by 12?
  14. 14.How many factors does 60 have?
  15. 15.What is the smallest number you must take away from 170 so that it divides exactly by 13?
  16. 16.What is the smallest number you must take away from 660 so that it divides exactly by 8?
  17. 17.What is the smallest number you must add to 732 so that it divides exactly by 9?
  18. 18.Which of these numbers divides exactly by 11? (a) 8778 (b) 7459 (c) 2554 (d) 2315
  19. 19.Which of these numbers divides exactly by 6? (a) 9140 (b) 3276 (c) 3860 (d) 5751
  20. 20.Which of these numbers divides exactly by 4? (a) 5631 (b) 3149 (c) 2210 (d) 1160
  21. 21.What is the smallest number you must take away from 757 so that it divides exactly by 12?
  22. 22.Which of these numbers divides exactly by 11? (a) 6897 (b) 4728 (c) 9678 (d) 8392
  23. 23.How many factors does 92 have?
  24. 24.What is the smallest number you must add to 548 so that it divides exactly by 11?
  25. 25.How many factors does 42 have?
  26. 26.What is the smallest number you must take away from 474 so that it divides exactly by 11?
  27. 27.What is the smallest number you must add to 111 so that it divides exactly by 8?
  28. 28.How many factors does 69 have?
  29. 29.What is the smallest number you must take away from 777 so that it divides exactly by 12?
  30. 30.What is the smallest number you must add to 628 so that it divides exactly by 13?
  31. 31.How many factors does 20 have?
  32. 32.What is the smallest number you must take away from 127 so that it divides exactly by 3?
  33. 33.How many factors does 87 have?
  34. 34.What is the smallest number you must take away from 737 so that it divides exactly by 8?
  35. 35.What is the smallest number you must take away from 539 so that it divides exactly by 9?
  36. 36.How many factors does 22 have?
  37. 37.Which of these numbers divides exactly by 11? (a) 3082 (b) 3630 (c) 1404 (d) 2709
  38. 38.Which of these numbers divides exactly by 11? (a) 8031 (b) 8949 (c) 7744 (d) 6926
  39. 39.How many factors does 88 have?
  40. 40.What is the smallest number you must take away from 210 so that it divides exactly by 12?

Answer key

  1. 12
  2. 3
  3. 6
  4. 2
  5. 11
  6. 4
  7. 6094
  8. 4
  9. 2
  10. 4
  11. 2
  12. 7434
  13. 7
  14. 12
  15. 1
  16. 4
  17. 6
  18. 8778
  19. 3276
  20. 1160
  21. 1
  22. 6897
  23. 6
  24. 2
  25. 8
  26. 1
  27. 1
  28. 4
  29. 9
  30. 9
  31. 6
  32. 1
  33. 4
  34. 1
  35. 8
  36. 4
  37. 3630
  38. 7744
  39. 8
  40. 6

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