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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 160 · 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 973 so that it divides exactly by 6?
  2. 2.What is the smallest number you must take away from 784 so that it divides exactly by 3?
  3. 3.What is the smallest number you must take away from 716 so that it divides exactly by 11?
  4. 4.What is the smallest number you must take away from 626 so that it divides exactly by 6?
  5. 5.How many factors does 34 have?
  6. 6.What is the smallest number you must add to 596 so that it divides exactly by 3?
  7. 7.Which of these numbers divides exactly by 3? (a) 7285 (b) 4249 (c) 5751 (d) 7834
  8. 8.Which of these numbers divides exactly by 9? (a) 4245 (b) 2086 (c) 3576 (d) 7992
  9. 9.Which of these numbers divides exactly by 6? (a) 9130 (b) 8515 (c) 7452 (d) 9524
  10. 10.What is the smallest number you must take away from 736 so that it divides exactly by 12?
  11. 11.What is the smallest number you must add to 448 so that it divides exactly by 6?
  12. 12.What is the smallest number you must take away from 254 so that it divides exactly by 6?
  13. 13.How many factors does 91 have?
  14. 14.What is the smallest number you must take away from 783 so that it divides exactly by 7?
  15. 15.How many factors does 98 have?
  16. 16.What is the smallest number you must add to 134 so that it divides exactly by 12?
  17. 17.How many factors does 15 have?
  18. 18.How many factors does 29 have?
  19. 19.What is the smallest number you must add to 470 so that it divides exactly by 13?
  20. 20.How many factors does 27 have?
  21. 21.How many factors does 25 have?
  22. 22.What is the smallest number you must add to 126 so that it divides exactly by 11?
  23. 23.Which of these numbers divides exactly by 8? (a) 3952 (b) 3865 (c) 3102 (d) 1548
  24. 24.How many factors does 32 have?
  25. 25.How many factors does 16 have?
  26. 26.How many factors does 89 have?
  27. 27.How many factors does 93 have?
  28. 28.What is the smallest number you must take away from 311 so that it divides exactly by 3?
  29. 29.What is the smallest number you must add to 787 so that it divides exactly by 6?
  30. 30.What is the smallest number you must take away from 303 so that it divides exactly by 4?
  31. 31.Which of these numbers divides exactly by 3? (a) 1128 (b) 6226 (c) 8425 (d) 4619
  32. 32.How many factors does 26 have?
  33. 33.What is the smallest number you must take away from 766 so that it divides exactly by 3?
  34. 34.How many factors does 70 have?
  35. 35.What is the smallest number you must add to 131 so that it divides exactly by 8?
  36. 36.Which of these numbers divides exactly by 6? (a) 7131 (b) 7296 (c) 9640 (d) 1760
  37. 37.How many factors does 17 have?
  38. 38.What is the smallest number you must add to 976 so that it divides exactly by 11?
  39. 39.How many factors does 45 have?
  40. 40.Which of these numbers divides exactly by 3? (a) 2963 (b) 3715 (c) 1243 (d) 4197

Answer key

  1. 1
  2. 1
  3. 1
  4. 2
  5. 4
  6. 1
  7. 5751
  8. 7992
  9. 7452
  10. 4
  11. 2
  12. 2
  13. 4
  14. 6
  15. 6
  16. 10
  17. 4
  18. 2
  19. 11
  20. 4
  21. 3
  22. 6
  23. 3952
  24. 6
  25. 5
  26. 2
  27. 4
  28. 2
  29. 5
  30. 3
  31. 1128
  32. 4
  33. 1
  34. 8
  35. 5
  36. 7296
  37. 2
  38. 3
  39. 6
  40. 4197

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