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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 95 · 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 177 so that it divides exactly by 4?
  2. 2.Which of these numbers divides exactly by 8? (a) 6152 (b) 8501 (c) 6123 (d) 2785
  3. 3.How many factors does 22 have?
  4. 4.What is the smallest number you must add to 170 so that it divides exactly by 3?
  5. 5.What is the smallest number you must take away from 787 so that it divides exactly by 7?
  6. 6.How many factors does 97 have?
  7. 7.Which of these numbers divides exactly by 3? (a) 7784 (b) 9598 (c) 2680 (d) 5793
  8. 8.Which of these numbers divides exactly by 4? (a) 3582 (b) 9082 (c) 2156 (d) 5593
  9. 9.What is the smallest number you must add to 274 so that it divides exactly by 4?
  10. 10.What is the smallest number you must add to 137 so that it divides exactly by 12?
  11. 11.How many factors does 68 have?
  12. 12.Which of these numbers divides exactly by 8? (a) 6024 (b) 3039 (c) 7660 (d) 4427
  13. 13.What is the smallest number you must take away from 457 so that it divides exactly by 4?
  14. 14.What is the smallest number you must take away from 286 so that it divides exactly by 7?
  15. 15.How many factors does 20 have?
  16. 16.How many factors does 26 have?
  17. 17.Which of these numbers divides exactly by 9? (a) 7425 (b) 1934 (c) 7648 (d) 7496
  18. 18.How many factors does 89 have?
  19. 19.What is the smallest number you must add to 214 so that it divides exactly by 11?
  20. 20.How many factors does 40 have?
  21. 21.Which of these numbers divides exactly by 3? (a) 2780 (b) 3994 (c) 8297 (d) 4959
  22. 22.How many factors does 15 have?
  23. 23.What is the smallest number you must take away from 526 so that it divides exactly by 3?
  24. 24.What is the smallest number you must take away from 349 so that it divides exactly by 6?
  25. 25.What is the smallest number you must add to 451 so that it divides exactly by 3?
  26. 26.What is the smallest number you must take away from 870 so that it divides exactly by 9?
  27. 27.What is the smallest number you must take away from 453 so that it divides exactly by 13?
  28. 28.What is the smallest number you must take away from 494 so that it divides exactly by 3?
  29. 29.Which of these numbers divides exactly by 8? (a) 1741 (b) 9171 (c) 9861 (d) 7384
  30. 30.How many factors does 99 have?
  31. 31.What is the smallest number you must add to 877 so that it divides exactly by 4?
  32. 32.How many factors does 18 have?
  33. 33.How many factors does 55 have?
  34. 34.How many factors does 41 have?
  35. 35.What is the smallest number you must add to 713 so that it divides exactly by 12?
  36. 36.Which of these numbers divides exactly by 11? (a) 7451 (b) 8500 (c) 9592 (d) 2624
  37. 37.What is the smallest number you must take away from 108 so that it divides exactly by 11?
  38. 38.How many factors does 57 have?
  39. 39.What is the smallest number you must add to 860 so that it divides exactly by 6?
  40. 40.Which of these numbers divides exactly by 11? (a) 4246 (b) 8229 (c) 1631 (d) 3626

Answer key

  1. 1
  2. 6152
  3. 4
  4. 1
  5. 3
  6. 2
  7. 5793
  8. 2156
  9. 2
  10. 7
  11. 6
  12. 6024
  13. 1
  14. 6
  15. 6
  16. 4
  17. 7425
  18. 2
  19. 6
  20. 8
  21. 4959
  22. 4
  23. 1
  24. 1
  25. 2
  26. 6
  27. 11
  28. 2
  29. 7384
  30. 6
  31. 3
  32. 6
  33. 4
  34. 2
  35. 7
  36. 9592
  37. 9
  38. 4
  39. 4
  40. 4246

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