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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 326 · 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 13 have?
  2. 2.How many factors does 69 have?
  3. 3.How many factors does 82 have?
  4. 4.How many factors does 35 have?
  5. 5.How many factors does 68 have?
  6. 6.What is the smallest number you must add to 147 so that it divides exactly by 4?
  7. 7.How many factors does 64 have?
  8. 8.What is the smallest number you must take away from 720 so that it divides exactly by 7?
  9. 9.Which of these numbers divides exactly by 11? (a) 5685 (b) 8178 (c) 6974 (d) 2458
  10. 10.What is the smallest number you must take away from 183 so that it divides exactly by 8?
  11. 11.How many factors does 30 have?
  12. 12.What is the smallest number you must take away from 786 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 393 so that it divides exactly by 8?
  14. 14.How many factors does 95 have?
  15. 15.How many factors does 21 have?
  16. 16.What is the smallest number you must add to 327 so that it divides exactly by 7?
  17. 17.What is the smallest number you must add to 200 so that it divides exactly by 9?
  18. 18.What is the smallest number you must take away from 338 so that it divides exactly by 8?
  19. 19.Which of these numbers divides exactly by 9? (a) 9619 (b) 8561 (c) 6991 (d) 1710
  20. 20.How many factors does 88 have?
  21. 21.What is the smallest number you must add to 700 so that it divides exactly by 11?
  22. 22.Which of these numbers divides exactly by 4? (a) 1970 (b) 1925 (c) 9035 (d) 8824
  23. 23.How many factors does 51 have?
  24. 24.Which of these numbers divides exactly by 6? (a) 7804 (b) 6119 (c) 9220 (d) 9054
  25. 25.Which of these numbers divides exactly by 4? (a) 1366 (b) 6448 (c) 1539 (d) 8150
  26. 26.Which of these numbers divides exactly by 6? (a) 6635 (b) 6849 (c) 8424 (d) 5089
  27. 27.How many factors does 92 have?
  28. 28.What is the smallest number you must add to 190 so that it divides exactly by 9?
  29. 29.What is the smallest number you must add to 238 so that it divides exactly by 12?
  30. 30.What is the smallest number you must take away from 967 so that it divides exactly by 9?
  31. 31.What is the smallest number you must take away from 129 so that it divides exactly by 4?
  32. 32.Which of these numbers divides exactly by 6? (a) 1122 (b) 3676 (c) 9311 (d) 8950
  33. 33.How many factors does 93 have?
  34. 34.Which of these numbers divides exactly by 9? (a) 9255 (b) 9089 (c) 4725 (d) 8152
  35. 35.How many factors does 49 have?
  36. 36.Which of these numbers divides exactly by 9? (a) 1100 (b) 3416 (c) 2213 (d) 4473
  37. 37.What is the smallest number you must add to 493 so that it divides exactly by 3?
  38. 38.Which of these numbers divides exactly by 6? (a) 5456 (b) 7495 (c) 4662 (d) 7135
  39. 39.How many factors does 48 have?
  40. 40.Which of these numbers divides exactly by 4? (a) 1894 (b) 3554 (c) 8240 (d) 5759

Answer key

  1. 2
  2. 4
  3. 4
  4. 4
  5. 6
  6. 1
  7. 7
  8. 6
  9. 6974
  10. 7
  11. 8
  12. 6
  13. 1
  14. 4
  15. 4
  16. 2
  17. 7
  18. 2
  19. 1710
  20. 8
  21. 4
  22. 8824
  23. 4
  24. 9054
  25. 6448
  26. 8424
  27. 6
  28. 8
  29. 2
  30. 4
  31. 1
  32. 1122
  33. 4
  34. 4725
  35. 3
  36. 4473
  37. 2
  38. 4662
  39. 10
  40. 8240

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