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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 19 · 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.Which of these numbers divides exactly by 4? (a) 6843 (b) 4981 (c) 6231 (d) 6840
  2. 2.What is the smallest number you must take away from 144 so that it divides exactly by 13?
  3. 3.How many factors does 77 have?
  4. 4.How many factors does 94 have?
  5. 5.How many factors does 41 have?
  6. 6.What is the smallest number you must add to 397 so that it divides exactly by 6?
  7. 7.How many factors does 34 have?
  8. 8.What is the smallest number you must add to 720 so that it divides exactly by 13?
  9. 9.How many factors does 87 have?
  10. 10.How many factors does 65 have?
  11. 11.Which of these numbers divides exactly by 4? (a) 8722 (b) 4294 (c) 2391 (d) 1828
  12. 12.Which of these numbers divides exactly by 9? (a) 9337 (b) 7181 (c) 2423 (d) 8982
  13. 13.What is the smallest number you must take away from 942 so that it divides exactly by 7?
  14. 14.What is the smallest number you must add to 903 so that it divides exactly by 12?
  15. 15.What is the smallest number you must add to 422 so that it divides exactly by 7?
  16. 16.How many factors does 98 have?
  17. 17.What is the smallest number you must take away from 230 so that it divides exactly by 3?
  18. 18.How many factors does 84 have?
  19. 19.Which of these numbers divides exactly by 9? (a) 9700 (b) 2447 (c) 5103 (d) 2971
  20. 20.What is the smallest number you must add to 875 so that it divides exactly by 4?
  21. 21.How many factors does 22 have?
  22. 22.What is the smallest number you must add to 645 so that it divides exactly by 12?
  23. 23.Which of these numbers divides exactly by 8? (a) 7297 (b) 6276 (c) 4666 (d) 3784
  24. 24.Which of these numbers divides exactly by 4? (a) 6550 (b) 7466 (c) 4771 (d) 4888
  25. 25.What is the smallest number you must take away from 718 so that it divides exactly by 4?
  26. 26.What is the smallest number you must add to 460 so that it divides exactly by 13?
  27. 27.What is the smallest number you must take away from 794 so that it divides exactly by 11?
  28. 28.Which of these numbers divides exactly by 3? (a) 4735 (b) 2215 (c) 9290 (d) 9039
  29. 29.What is the smallest number you must add to 125 so that it divides exactly by 4?
  30. 30.What is the smallest number you must add to 795 so that it divides exactly by 6?
  31. 31.What is the smallest number you must take away from 512 so that it divides exactly by 9?
  32. 32.How many factors does 32 have?
  33. 33.How many factors does 63 have?
  34. 34.Which of these numbers divides exactly by 3? (a) 6125 (b) 9778 (c) 2619 (d) 3616
  35. 35.How many factors does 18 have?
  36. 36.Which of these numbers divides exactly by 6? (a) 5300 (b) 4285 (c) 1659 (d) 8784
  37. 37.What is the smallest number you must add to 125 so that it divides exactly by 7?
  38. 38.How many factors does 43 have?
  39. 39.What is the smallest number you must take away from 898 so that it divides exactly by 3?
  40. 40.What is the smallest number you must add to 749 so that it divides exactly by 12?

Answer key

  1. 6840
  2. 1
  3. 4
  4. 4
  5. 2
  6. 5
  7. 4
  8. 8
  9. 4
  10. 4
  11. 1828
  12. 8982
  13. 4
  14. 9
  15. 5
  16. 6
  17. 2
  18. 12
  19. 5103
  20. 1
  21. 4
  22. 3
  23. 3784
  24. 4888
  25. 2
  26. 8
  27. 2
  28. 9039
  29. 3
  30. 3
  31. 8
  32. 6
  33. 6
  34. 2619
  35. 6
  36. 8784
  37. 1
  38. 2
  39. 1
  40. 7

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