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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 12 · 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 17 have?
  2. 2.How many factors does 53 have?
  3. 3.What is the smallest number you must add to 984 so that it divides exactly by 7?
  4. 4.How many factors does 30 have?
  5. 5.How many factors does 67 have?
  6. 6.Which of these numbers divides exactly by 9? (a) 2460 (b) 1802 (c) 2363 (d) 5121
  7. 7.What is the smallest number you must add to 184 so that it divides exactly by 9?
  8. 8.Which of these numbers divides exactly by 6? (a) 8207 (b) 9215 (c) 3462 (d) 1171
  9. 9.Which of these numbers divides exactly by 6? (a) 8309 (b) 8912 (c) 7296 (d) 8167
  10. 10.How many factors does 84 have?
  11. 11.How many factors does 66 have?
  12. 12.How many factors does 73 have?
  13. 13.How many factors does 15 have?
  14. 14.How many factors does 13 have?
  15. 15.What is the smallest number you must take away from 380 so that it divides exactly by 13?
  16. 16.How many factors does 19 have?
  17. 17.What is the smallest number you must take away from 459 so that it divides exactly by 11?
  18. 18.What is the smallest number you must take away from 749 so that it divides exactly by 13?
  19. 19.What is the smallest number you must add to 974 so that it divides exactly by 7?
  20. 20.What is the smallest number you must add to 254 so that it divides exactly by 11?
  21. 21.What is the smallest number you must take away from 872 so that it divides exactly by 12?
  22. 22.How many factors does 16 have?
  23. 23.What is the smallest number you must add to 139 so that it divides exactly by 8?
  24. 24.What is the smallest number you must take away from 316 so that it divides exactly by 3?
  25. 25.What is the smallest number you must take away from 782 so that it divides exactly by 8?
  26. 26.Which of these numbers divides exactly by 11? (a) 2799 (b) 9767 (c) 7640 (d) 5643
  27. 27.What is the smallest number you must take away from 280 so that it divides exactly by 13?
  28. 28.What is the smallest number you must take away from 919 so that it divides exactly by 13?
  29. 29.What is the smallest number you must add to 933 so that it divides exactly by 6?
  30. 30.What is the smallest number you must add to 768 so that it divides exactly by 9?
  31. 31.How many factors does 31 have?
  32. 32.What is the smallest number you must add to 365 so that it divides exactly by 9?
  33. 33.What is the smallest number you must take away from 625 so that it divides exactly by 13?
  34. 34.What is the smallest number you must add to 555 so that it divides exactly by 9?
  35. 35.What is the smallest number you must add to 297 so that it divides exactly by 4?
  36. 36.What is the smallest number you must add to 425 so that it divides exactly by 9?
  37. 37.What is the smallest number you must take away from 254 so that it divides exactly by 11?
  38. 38.What is the smallest number you must add to 875 so that it divides exactly by 11?
  39. 39.What is the smallest number you must take away from 590 so that it divides exactly by 12?
  40. 40.What is the smallest number you must take away from 202 so that it divides exactly by 7?

Answer key

  1. 2
  2. 2
  3. 3
  4. 8
  5. 2
  6. 5121
  7. 5
  8. 3462
  9. 7296
  10. 12
  11. 8
  12. 2
  13. 4
  14. 2
  15. 3
  16. 2
  17. 8
  18. 8
  19. 6
  20. 10
  21. 8
  22. 5
  23. 5
  24. 1
  25. 6
  26. 5643
  27. 7
  28. 9
  29. 3
  30. 6
  31. 2
  32. 4
  33. 1
  34. 3
  35. 3
  36. 7
  37. 1
  38. 5
  39. 2
  40. 6

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