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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 9 · 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 41 have?
  2. 2.What is the smallest number you must add to 344 so that it divides exactly by 7?
  3. 3.Which of these numbers divides exactly by 6? (a) 1897 (b) 6348 (c) 7244 (d) 9844
  4. 4.How many factors does 90 have?
  5. 5.How many factors does 76 have?
  6. 6.How many factors does 65 have?
  7. 7.Which of these numbers divides exactly by 11? (a) 2893 (b) 4726 (c) 6319 (d) 9121
  8. 8.How many factors does 85 have?
  9. 9.Which of these numbers divides exactly by 3? (a) 8038 (b) 7682 (c) 2747 (d) 2229
  10. 10.Which of these numbers divides exactly by 11? (a) 3960 (b) 4430 (c) 1569 (d) 9015
  11. 11.What is the smallest number you must take away from 269 so that it divides exactly by 8?
  12. 12.Which of these numbers divides exactly by 3? (a) 2936 (b) 6132 (c) 2564 (d) 5353
  13. 13.How many factors does 93 have?
  14. 14.What is the smallest number you must take away from 344 so that it divides exactly by 7?
  15. 15.How many factors does 64 have?
  16. 16.How many factors does 49 have?
  17. 17.What is the smallest number you must take away from 157 so that it divides exactly by 9?
  18. 18.How many factors does 29 have?
  19. 19.How many factors does 89 have?
  20. 20.How many factors does 47 have?
  21. 21.How many factors does 87 have?
  22. 22.What is the smallest number you must add to 613 so that it divides exactly by 7?
  23. 23.Which of these numbers divides exactly by 11? (a) 9431 (b) 2327 (c) 6664 (d) 5676
  24. 24.How many factors does 20 have?
  25. 25.What is the smallest number you must take away from 312 so that it divides exactly by 11?
  26. 26.Which of these numbers divides exactly by 8? (a) 2925 (b) 1333 (c) 8272 (d) 3927
  27. 27.What is the smallest number you must take away from 971 so that it divides exactly by 11?
  28. 28.What is the smallest number you must add to 234 so that it divides exactly by 8?
  29. 29.Which of these numbers divides exactly by 4? (a) 9913 (b) 6763 (c) 3024 (d) 7062
  30. 30.What is the smallest number you must take away from 234 so that it divides exactly by 4?
  31. 31.How many factors does 98 have?
  32. 32.How many factors does 28 have?
  33. 33.What is the smallest number you must add to 865 so that it divides exactly by 8?
  34. 34.Which of these numbers divides exactly by 3? (a) 7940 (b) 4112 (c) 8110 (d) 7983
  35. 35.What is the smallest number you must add to 681 so that it divides exactly by 6?
  36. 36.What is the smallest number you must take away from 322 so that it divides exactly by 6?
  37. 37.How many factors does 70 have?
  38. 38.How many factors does 55 have?
  39. 39.What is the smallest number you must take away from 235 so that it divides exactly by 12?
  40. 40.How many factors does 24 have?

Answer key

  1. 2
  2. 6
  3. 6348
  4. 12
  5. 6
  6. 4
  7. 2893
  8. 4
  9. 2229
  10. 3960
  11. 5
  12. 6132
  13. 4
  14. 1
  15. 7
  16. 3
  17. 4
  18. 2
  19. 2
  20. 2
  21. 4
  22. 3
  23. 5676
  24. 6
  25. 4
  26. 8272
  27. 3
  28. 6
  29. 3024
  30. 2
  31. 6
  32. 6
  33. 7
  34. 7983
  35. 3
  36. 4
  37. 8
  38. 4
  39. 7
  40. 8

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