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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 309 · 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 829 so that it divides exactly by 8?
  2. 2.What is the smallest number you must add to 121 so that it divides exactly by 3?
  3. 3.How many factors does 41 have?
  4. 4.What is the smallest number you must add to 505 so that it divides exactly by 9?
  5. 5.How many factors does 12 have?
  6. 6.How many factors does 48 have?
  7. 7.What is the smallest number you must add to 237 so that it divides exactly by 6?
  8. 8.What is the smallest number you must take away from 200 so that it divides exactly by 11?
  9. 9.What is the smallest number you must add to 961 so that it divides exactly by 12?
  10. 10.What is the smallest number you must add to 900 so that it divides exactly by 8?
  11. 11.How many factors does 60 have?
  12. 12.What is the smallest number you must add to 647 so that it divides exactly by 13?
  13. 13.What is the smallest number you must add to 213 so that it divides exactly by 12?
  14. 14.Which of these numbers divides exactly by 6? (a) 4569 (b) 4536 (c) 3457 (d) 6723
  15. 15.How many factors does 16 have?
  16. 16.Which of these numbers divides exactly by 11? (a) 3083 (b) 2794 (c) 2826 (d) 5707
  17. 17.How many factors does 78 have?
  18. 18.How many factors does 53 have?
  19. 19.What is the smallest number you must take away from 846 so that it divides exactly by 13?
  20. 20.How many factors does 83 have?
  21. 21.How many factors does 21 have?
  22. 22.What is the smallest number you must add to 459 so that it divides exactly by 8?
  23. 23.How many factors does 91 have?
  24. 24.How many factors does 37 have?
  25. 25.What is the smallest number you must take away from 906 so that it divides exactly by 7?
  26. 26.What is the smallest number you must take away from 837 so that it divides exactly by 12?
  27. 27.What is the smallest number you must add to 255 so that it divides exactly by 11?
  28. 28.What is the smallest number you must take away from 115 so that it divides exactly by 13?
  29. 29.How many factors does 36 have?
  30. 30.How many factors does 67 have?
  31. 31.What is the smallest number you must add to 405 so that it divides exactly by 7?
  32. 32.How many factors does 68 have?
  33. 33.What is the smallest number you must add to 316 so that it divides exactly by 6?
  34. 34.How many factors does 98 have?
  35. 35.What is the smallest number you must take away from 494 so that it divides exactly by 4?
  36. 36.What is the smallest number you must add to 496 so that it divides exactly by 12?
  37. 37.Which of these numbers divides exactly by 3? (a) 9138 (b) 2450 (c) 7055 (d) 6188
  38. 38.What is the smallest number you must take away from 505 so that it divides exactly by 3?
  39. 39.What is the smallest number you must take away from 905 so that it divides exactly by 7?
  40. 40.Which of these numbers divides exactly by 4? (a) 5238 (b) 3491 (c) 9036 (d) 7930

Answer key

  1. 5
  2. 2
  3. 2
  4. 8
  5. 6
  6. 10
  7. 3
  8. 2
  9. 11
  10. 4
  11. 12
  12. 3
  13. 3
  14. 4536
  15. 5
  16. 2794
  17. 8
  18. 2
  19. 1
  20. 2
  21. 4
  22. 5
  23. 4
  24. 2
  25. 3
  26. 9
  27. 9
  28. 11
  29. 9
  30. 2
  31. 1
  32. 6
  33. 2
  34. 6
  35. 2
  36. 8
  37. 9138
  38. 1
  39. 2
  40. 9036

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