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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 159 · 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 38 have?
  3. 3.What is the smallest number you must take away from 533 so that it divides exactly by 3?
  4. 4.What is the smallest number you must add to 178 so that it divides exactly by 7?
  5. 5.What is the smallest number you must add to 293 so that it divides exactly by 6?
  6. 6.Which of these numbers divides exactly by 4? (a) 9771 (b) 2193 (c) 9740 (d) 3546
  7. 7.What is the smallest number you must add to 899 so that it divides exactly by 8?
  8. 8.How many factors does 27 have?
  9. 9.How many factors does 76 have?
  10. 10.Which of these numbers divides exactly by 6? (a) 3521 (b) 3294 (c) 8037 (d) 9603
  11. 11.How many factors does 26 have?
  12. 12.What is the smallest number you must add to 547 so that it divides exactly by 4?
  13. 13.What is the smallest number you must add to 191 so that it divides exactly by 7?
  14. 14.How many factors does 21 have?
  15. 15.Which of these numbers divides exactly by 6? (a) 7034 (b) 5414 (c) 9008 (d) 3414
  16. 16.Which of these numbers divides exactly by 6? (a) 5126 (b) 3856 (c) 9419 (d) 3732
  17. 17.Which of these numbers divides exactly by 6? (a) 3176 (b) 3317 (c) 8636 (d) 8136
  18. 18.How many factors does 93 have?
  19. 19.How many factors does 14 have?
  20. 20.Which of these numbers divides exactly by 9? (a) 6082 (b) 6595 (c) 6214 (d) 9990
  21. 21.How many factors does 60 have?
  22. 22.Which of these numbers divides exactly by 9? (a) 1955 (b) 3668 (c) 5346 (d) 4408
  23. 23.What is the smallest number you must take away from 311 so that it divides exactly by 8?
  24. 24.What is the smallest number you must take away from 937 so that it divides exactly by 12?
  25. 25.What is the smallest number you must take away from 631 so that it divides exactly by 4?
  26. 26.How many factors does 13 have?
  27. 27.How many factors does 100 have?
  28. 28.What is the smallest number you must add to 526 so that it divides exactly by 6?
  29. 29.What is the smallest number you must add to 575 so that it divides exactly by 13?
  30. 30.Which of these numbers divides exactly by 6? (a) 3854 (b) 8215 (c) 3636 (d) 5811
  31. 31.How many factors does 32 have?
  32. 32.What is the smallest number you must add to 902 so that it divides exactly by 7?
  33. 33.What is the smallest number you must add to 490 so that it divides exactly by 6?
  34. 34.How many factors does 20 have?
  35. 35.Which of these numbers divides exactly by 11? (a) 5144 (b) 2909 (c) 5082 (d) 2697
  36. 36.What is the smallest number you must add to 941 so that it divides exactly by 3?
  37. 37.What is the smallest number you must add to 386 so that it divides exactly by 12?
  38. 38.What is the smallest number you must take away from 523 so that it divides exactly by 4?
  39. 39.Which of these numbers divides exactly by 3? (a) 1184 (b) 1186 (c) 7125 (d) 6610
  40. 40.Which of these numbers divides exactly by 4? (a) 6594 (b) 7925 (c) 2549 (d) 5148

Answer key

  1. 2
  2. 4
  3. 2
  4. 4
  5. 1
  6. 9740
  7. 5
  8. 4
  9. 6
  10. 3294
  11. 4
  12. 1
  13. 5
  14. 4
  15. 3414
  16. 3732
  17. 8136
  18. 4
  19. 4
  20. 9990
  21. 12
  22. 5346
  23. 7
  24. 1
  25. 3
  26. 2
  27. 9
  28. 2
  29. 10
  30. 3636
  31. 6
  32. 1
  33. 2
  34. 6
  35. 5082
  36. 1
  37. 10
  38. 3
  39. 7125
  40. 5148

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