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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 260 · 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 take away from 887 so that it divides exactly by 4?
  2. 2.How many factors does 64 have?
  3. 3.What is the smallest number you must take away from 300 so that it divides exactly by 7?
  4. 4.What is the smallest number you must take away from 898 so that it divides exactly by 13?
  5. 5.What is the smallest number you must add to 571 so that it divides exactly by 9?
  6. 6.How many factors does 51 have?
  7. 7.How many factors does 44 have?
  8. 8.What is the smallest number you must add to 985 so that it divides exactly by 3?
  9. 9.What is the smallest number you must add to 332 so that it divides exactly by 12?
  10. 10.How many factors does 72 have?
  11. 11.How many factors does 54 have?
  12. 12.How many factors does 33 have?
  13. 13.How many factors does 56 have?
  14. 14.How many factors does 42 have?
  15. 15.What is the smallest number you must add to 385 so that it divides exactly by 3?
  16. 16.Which of these numbers divides exactly by 6? (a) 3073 (b) 5950 (c) 3888 (d) 4073
  17. 17.Which of these numbers divides exactly by 6? (a) 3340 (b) 5210 (c) 4482 (d) 8662
  18. 18.What is the smallest number you must take away from 116 so that it divides exactly by 12?
  19. 19.How many factors does 49 have?
  20. 20.What is the smallest number you must add to 653 so that it divides exactly by 13?
  21. 21.What is the smallest number you must add to 464 so that it divides exactly by 9?
  22. 22.What is the smallest number you must take away from 416 so that it divides exactly by 6?
  23. 23.What is the smallest number you must take away from 421 so that it divides exactly by 13?
  24. 24.What is the smallest number you must add to 545 so that it divides exactly by 12?
  25. 25.How many factors does 13 have?
  26. 26.How many factors does 85 have?
  27. 27.What is the smallest number you must add to 822 so that it divides exactly by 4?
  28. 28.What is the smallest number you must take away from 330 so that it divides exactly by 7?
  29. 29.Which of these numbers divides exactly by 11? (a) 7647 (b) 5005 (c) 9390 (d) 9342
  30. 30.What is the smallest number you must add to 786 so that it divides exactly by 7?
  31. 31.Which of these numbers divides exactly by 6? (a) 6508 (b) 1770 (c) 4672 (d) 9685
  32. 32.What is the smallest number you must take away from 505 so that it divides exactly by 12?
  33. 33.What is the smallest number you must take away from 109 so that it divides exactly by 6?
  34. 34.How many factors does 20 have?
  35. 35.What is the smallest number you must add to 752 so that it divides exactly by 11?
  36. 36.What is the smallest number you must add to 745 so that it divides exactly by 3?
  37. 37.What is the smallest number you must take away from 845 so that it divides exactly by 12?
  38. 38.Which of these numbers divides exactly by 8? (a) 1308 (b) 8243 (c) 7756 (d) 6944
  39. 39.How many factors does 63 have?
  40. 40.What is the smallest number you must add to 419 so that it divides exactly by 6?

Answer key

  1. 3
  2. 7
  3. 6
  4. 1
  5. 5
  6. 4
  7. 6
  8. 2
  9. 4
  10. 12
  11. 8
  12. 4
  13. 8
  14. 8
  15. 2
  16. 3888
  17. 4482
  18. 8
  19. 3
  20. 10
  21. 4
  22. 2
  23. 5
  24. 7
  25. 2
  26. 4
  27. 2
  28. 1
  29. 5005
  30. 5
  31. 1770
  32. 1
  33. 1
  34. 6
  35. 7
  36. 2
  37. 5
  38. 6944
  39. 6
  40. 1

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