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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 229 · 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 add to 109 so that it divides exactly by 11?
  2. 2.How many factors does 12 have?
  3. 3.How many factors does 33 have?
  4. 4.What is the smallest number you must take away from 881 so that it divides exactly by 13?
  5. 5.How many factors does 77 have?
  6. 6.How many factors does 29 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 8474 (b) 6611 (c) 5628 (d) 2687
  8. 8.What is the smallest number you must add to 209 so that it divides exactly by 8?
  9. 9.What is the smallest number you must add to 655 so that it divides exactly by 9?
  10. 10.What is the smallest number you must add to 833 so that it divides exactly by 13?
  11. 11.What is the smallest number you must take away from 276 so that it divides exactly by 13?
  12. 12.How many factors does 50 have?
  13. 13.How many factors does 36 have?
  14. 14.What is the smallest number you must take away from 494 so that it divides exactly by 6?
  15. 15.Which of these numbers divides exactly by 6? (a) 3287 (b) 9765 (c) 8877 (d) 9102
  16. 16.What is the smallest number you must add to 397 so that it divides exactly by 4?
  17. 17.How many factors does 67 have?
  18. 18.What is the smallest number you must add to 620 so that it divides exactly by 12?
  19. 19.What is the smallest number you must take away from 264 so that it divides exactly by 13?
  20. 20.Which of these numbers divides exactly by 11? (a) 5025 (b) 9537 (c) 4084 (d) 3991
  21. 21.How many factors does 46 have?
  22. 22.What is the smallest number you must add to 739 so that it divides exactly by 13?
  23. 23.Which of these numbers divides exactly by 3? (a) 8098 (b) 1946 (c) 8191 (d) 7029
  24. 24.What is the smallest number you must add to 951 so that it divides exactly by 6?
  25. 25.What is the smallest number you must take away from 277 so that it divides exactly by 4?
  26. 26.What is the smallest number you must add to 391 so that it divides exactly by 4?
  27. 27.What is the smallest number you must take away from 105 so that it divides exactly by 9?
  28. 28.What is the smallest number you must take away from 651 so that it divides exactly by 13?
  29. 29.What is the smallest number you must take away from 980 so that it divides exactly by 3?
  30. 30.What is the smallest number you must take away from 539 so that it divides exactly by 4?
  31. 31.Which of these numbers divides exactly by 9? (a) 8087 (b) 2678 (c) 2860 (d) 5778
  32. 32.How many factors does 37 have?
  33. 33.How many factors does 14 have?
  34. 34.What is the smallest number you must add to 181 so that it divides exactly by 13?
  35. 35.What is the smallest number you must take away from 237 so that it divides exactly by 13?
  36. 36.How many factors does 23 have?
  37. 37.How many factors does 32 have?
  38. 38.What is the smallest number you must take away from 208 so that it divides exactly by 6?
  39. 39.How many factors does 30 have?
  40. 40.What is the smallest number you must take away from 811 so that it divides exactly by 3?

Answer key

  1. 1
  2. 6
  3. 4
  4. 10
  5. 4
  6. 2
  7. 6611
  8. 7
  9. 2
  10. 12
  11. 3
  12. 6
  13. 9
  14. 2
  15. 9102
  16. 3
  17. 2
  18. 4
  19. 4
  20. 9537
  21. 4
  22. 2
  23. 7029
  24. 3
  25. 1
  26. 1
  27. 6
  28. 1
  29. 2
  30. 3
  31. 5778
  32. 2
  33. 4
  34. 1
  35. 3
  36. 2
  37. 6
  38. 4
  39. 8
  40. 1

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