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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 64 · 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 707 so that it divides exactly by 6?
  2. 2.Which of these numbers divides exactly by 11? (a) 6123 (b) 7152 (c) 7343 (d) 3465
  3. 3.What is the smallest number you must add to 280 so that it divides exactly by 3?
  4. 4.How many factors does 72 have?
  5. 5.How many factors does 25 have?
  6. 6.How many factors does 53 have?
  7. 7.What is the smallest number you must take away from 696 so that it divides exactly by 13?
  8. 8.How many factors does 86 have?
  9. 9.Which of these numbers divides exactly by 4? (a) 3456 (b) 6357 (c) 7929 (d) 5661
  10. 10.What is the smallest number you must take away from 479 so that it divides exactly by 3?
  11. 11.How many factors does 37 have?
  12. 12.Which of these numbers divides exactly by 6? (a) 2058 (b) 5897 (c) 7881 (d) 4105
  13. 13.What is the smallest number you must add to 232 so that it divides exactly by 13?
  14. 14.How many factors does 28 have?
  15. 15.How many factors does 63 have?
  16. 16.How many factors does 93 have?
  17. 17.Which of these numbers divides exactly by 6? (a) 5050 (b) 7875 (c) 8334 (d) 3116
  18. 18.What is the smallest number you must add to 393 so that it divides exactly by 7?
  19. 19.Which of these numbers divides exactly by 3? (a) 7098 (b) 8482 (c) 7816 (d) 8096
  20. 20.What is the smallest number you must take away from 197 so that it divides exactly by 12?
  21. 21.What is the smallest number you must take away from 586 so that it divides exactly by 6?
  22. 22.How many factors does 35 have?
  23. 23.What is the smallest number you must add to 853 so that it divides exactly by 6?
  24. 24.Which of these numbers divides exactly by 8? (a) 2297 (b) 6116 (c) 8008 (d) 2108
  25. 25.How many factors does 67 have?
  26. 26.Which of these numbers divides exactly by 3? (a) 3953 (b) 5943 (c) 5939 (d) 1847
  27. 27.Which of these numbers divides exactly by 3? (a) 1061 (b) 9401 (c) 1819 (d) 2784
  28. 28.How many factors does 19 have?
  29. 29.What is the smallest number you must add to 277 so that it divides exactly by 13?
  30. 30.Which of these numbers divides exactly by 9? (a) 1625 (b) 1305 (c) 6825 (d) 9895
  31. 31.How many factors does 26 have?
  32. 32.How many factors does 22 have?
  33. 33.What is the smallest number you must take away from 523 so that it divides exactly by 13?
  34. 34.What is the smallest number you must take away from 177 so that it divides exactly by 4?
  35. 35.What is the smallest number you must add to 908 so that it divides exactly by 6?
  36. 36.What is the smallest number you must add to 897 so that it divides exactly by 4?
  37. 37.What is the smallest number you must add to 302 so that it divides exactly by 12?
  38. 38.What is the smallest number you must take away from 573 so that it divides exactly by 8?
  39. 39.How many factors does 65 have?
  40. 40.Which of these numbers divides exactly by 4? (a) 2326 (b) 7340 (c) 8803 (d) 2355

Answer key

  1. 1
  2. 3465
  3. 2
  4. 12
  5. 3
  6. 2
  7. 7
  8. 4
  9. 3456
  10. 2
  11. 2
  12. 2058
  13. 2
  14. 6
  15. 6
  16. 4
  17. 8334
  18. 6
  19. 7098
  20. 5
  21. 4
  22. 4
  23. 5
  24. 8008
  25. 2
  26. 5943
  27. 2784
  28. 2
  29. 9
  30. 1305
  31. 4
  32. 4
  33. 3
  34. 1
  35. 4
  36. 3
  37. 10
  38. 5
  39. 4
  40. 7340

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