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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 255 · 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 795 so that it divides exactly by 12?
  2. 2.What is the smallest number you must take away from 126 so that it divides exactly by 11?
  3. 3.What is the smallest number you must add to 788 so that it divides exactly by 3?
  4. 4.How many factors does 59 have?
  5. 5.How many factors does 87 have?
  6. 6.Which of these numbers divides exactly by 8? (a) 5589 (b) 3726 (c) 5115 (d) 9304
  7. 7.What is the smallest number you must take away from 690 so that it divides exactly by 7?
  8. 8.How many factors does 94 have?
  9. 9.What is the smallest number you must take away from 327 so that it divides exactly by 7?
  10. 10.What is the smallest number you must add to 593 so that it divides exactly by 6?
  11. 11.How many factors does 41 have?
  12. 12.How many factors does 19 have?
  13. 13.How many factors does 48 have?
  14. 14.How many factors does 53 have?
  15. 15.Which of these numbers divides exactly by 6? (a) 9081 (b) 4108 (c) 6900 (d) 5786
  16. 16.How many factors does 75 have?
  17. 17.What is the smallest number you must take away from 263 so that it divides exactly by 9?
  18. 18.Which of these numbers divides exactly by 9? (a) 4212 (b) 9838 (c) 2044 (d) 7283
  19. 19.How many factors does 25 have?
  20. 20.Which of these numbers divides exactly by 3? (a) 6560 (b) 9783 (c) 7591 (d) 9560
  21. 21.What is the smallest number you must add to 772 so that it divides exactly by 8?
  22. 22.Which of these numbers divides exactly by 3? (a) 2003 (b) 5874 (c) 8029 (d) 7667
  23. 23.What is the smallest number you must take away from 811 so that it divides exactly by 6?
  24. 24.How many factors does 56 have?
  25. 25.What is the smallest number you must add to 553 so that it divides exactly by 3?
  26. 26.Which of these numbers divides exactly by 6? (a) 8149 (b) 7584 (c) 3502 (d) 8675
  27. 27.What is the smallest number you must take away from 380 so that it divides exactly by 6?
  28. 28.Which of these numbers divides exactly by 6? (a) 3398 (b) 1499 (c) 4452 (d) 7712
  29. 29.How many factors does 58 have?
  30. 30.What is the smallest number you must add to 725 so that it divides exactly by 3?
  31. 31.What is the smallest number you must take away from 962 so that it divides exactly by 6?
  32. 32.What is the smallest number you must add to 410 so that it divides exactly by 9?
  33. 33.How many factors does 92 have?
  34. 34.Which of these numbers divides exactly by 4? (a) 2511 (b) 9389 (c) 8636 (d) 1543
  35. 35.How many factors does 22 have?
  36. 36.What is the smallest number you must take away from 577 so that it divides exactly by 11?
  37. 37.What is the smallest number you must add to 884 so that it divides exactly by 7?
  38. 38.How many factors does 97 have?
  39. 39.What is the smallest number you must take away from 182 so that it divides exactly by 9?
  40. 40.Which of these numbers divides exactly by 11? (a) 2662 (b) 1143 (c) 3439 (d) 7142

Answer key

  1. 3
  2. 5
  3. 1
  4. 2
  5. 4
  6. 9304
  7. 4
  8. 4
  9. 5
  10. 1
  11. 2
  12. 2
  13. 10
  14. 2
  15. 6900
  16. 6
  17. 2
  18. 4212
  19. 3
  20. 9783
  21. 4
  22. 5874
  23. 1
  24. 8
  25. 2
  26. 7584
  27. 2
  28. 4452
  29. 4
  30. 1
  31. 2
  32. 4
  33. 6
  34. 8636
  35. 4
  36. 5
  37. 5
  38. 2
  39. 2
  40. 2662

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