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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 47 · 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 664 so that it divides exactly by 6?
  2. 2.How many factors does 33 have?
  3. 3.Which of these numbers divides exactly by 6? (a) 2753 (b) 8415 (c) 8912 (d) 3708
  4. 4.How many factors does 95 have?
  5. 5.What is the smallest number you must take away from 339 so that it divides exactly by 9?
  6. 6.What is the smallest number you must take away from 908 so that it divides exactly by 3?
  7. 7.How many factors does 34 have?
  8. 8.How many factors does 91 have?
  9. 9.How many factors does 20 have?
  10. 10.Which of these numbers divides exactly by 11? (a) 4954 (b) 7492 (c) 3912 (d) 7051
  11. 11.How many factors does 44 have?
  12. 12.What is the smallest number you must add to 993 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 796 so that it divides exactly by 9?
  14. 14.How many factors does 74 have?
  15. 15.How many factors does 23 have?
  16. 16.What is the smallest number you must add to 996 so that it divides exactly by 9?
  17. 17.What is the smallest number you must add to 868 so that it divides exactly by 6?
  18. 18.How many factors does 25 have?
  19. 19.Which of these numbers divides exactly by 6? (a) 4578 (b) 5343 (c) 5629 (d) 4310
  20. 20.Which of these numbers divides exactly by 4? (a) 9148 (b) 5434 (c) 7915 (d) 7290
  21. 21.What is the smallest number you must add to 439 so that it divides exactly by 3?
  22. 22.How many factors does 38 have?
  23. 23.What is the smallest number you must add to 177 so that it divides exactly by 13?
  24. 24.What is the smallest number you must take away from 972 so that it divides exactly by 8?
  25. 25.What is the smallest number you must add to 943 so that it divides exactly by 4?
  26. 26.Which of these numbers divides exactly by 11? (a) 1333 (b) 6479 (c) 2448 (d) 3015
  27. 27.How many factors does 71 have?
  28. 28.What is the smallest number you must take away from 562 so that it divides exactly by 11?
  29. 29.What is the smallest number you must take away from 886 so that it divides exactly by 11?
  30. 30.Which of these numbers divides exactly by 3? (a) 8441 (b) 5225 (c) 5135 (d) 5598
  31. 31.Which of these numbers divides exactly by 3? (a) 7391 (b) 3091 (c) 6427 (d) 7068
  32. 32.What is the smallest number you must take away from 819 so that it divides exactly by 12?
  33. 33.What is the smallest number you must add to 148 so that it divides exactly by 6?
  34. 34.Which of these numbers divides exactly by 3? (a) 9465 (b) 2782 (c) 7960 (d) 7496
  35. 35.Which of these numbers divides exactly by 8? (a) 2315 (b) 9101 (c) 3360 (d) 2972
  36. 36.How many factors does 49 have?
  37. 37.What is the smallest number you must add to 122 so that it divides exactly by 6?
  38. 38.What is the smallest number you must add to 131 so that it divides exactly by 6?
  39. 39.What is the smallest number you must take away from 457 so that it divides exactly by 13?
  40. 40.How many factors does 47 have?

Answer key

  1. 2
  2. 4
  3. 3708
  4. 4
  5. 6
  6. 2
  7. 4
  8. 4
  9. 6
  10. 7051
  11. 6
  12. 8
  13. 4
  14. 4
  15. 2
  16. 3
  17. 2
  18. 3
  19. 4578
  20. 9148
  21. 2
  22. 4
  23. 5
  24. 4
  25. 1
  26. 6479
  27. 2
  28. 1
  29. 6
  30. 5598
  31. 7068
  32. 3
  33. 2
  34. 9465
  35. 3360
  36. 3
  37. 4
  38. 1
  39. 2
  40. 2

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