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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 97 · 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 6? (a) 8797 (b) 9111 (c) 2999 (d) 7764
  2. 2.What is the smallest number you must take away from 325 so that it divides exactly by 7?
  3. 3.What is the smallest number you must take away from 175 so that it divides exactly by 4?
  4. 4.Which of these numbers divides exactly by 4? (a) 3033 (b) 9180 (c) 5982 (d) 2983
  5. 5.What is the smallest number you must add to 567 so that it divides exactly by 8?
  6. 6.How many factors does 70 have?
  7. 7.How many factors does 16 have?
  8. 8.Which of these numbers divides exactly by 3? (a) 2959 (b) 1899 (c) 2039 (d) 4789
  9. 9.How many factors does 19 have?
  10. 10.What is the smallest number you must take away from 803 so that it divides exactly by 3?
  11. 11.What is the smallest number you must add to 119 so that it divides exactly by 4?
  12. 12.What is the smallest number you must take away from 292 so that it divides exactly by 3?
  13. 13.What is the smallest number you must take away from 620 so that it divides exactly by 8?
  14. 14.What is the smallest number you must take away from 993 so that it divides exactly by 9?
  15. 15.Which of these numbers divides exactly by 9? (a) 4845 (b) 9598 (c) 3780 (d) 8671
  16. 16.Which of these numbers divides exactly by 4? (a) 6849 (b) 8535 (c) 1719 (d) 8828
  17. 17.How many factors does 46 have?
  18. 18.How many factors does 48 have?
  19. 19.Which of these numbers divides exactly by 8? (a) 5620 (b) 3443 (c) 3008 (d) 3813
  20. 20.What is the smallest number you must add to 554 so that it divides exactly by 13?
  21. 21.How many factors does 27 have?
  22. 22.How many factors does 58 have?
  23. 23.What is the smallest number you must add to 645 so that it divides exactly by 12?
  24. 24.How many factors does 78 have?
  25. 25.What is the smallest number you must take away from 189 so that it divides exactly by 8?
  26. 26.What is the smallest number you must add to 245 so that it divides exactly by 3?
  27. 27.How many factors does 25 have?
  28. 28.What is the smallest number you must add to 590 so that it divides exactly by 6?
  29. 29.What is the smallest number you must take away from 523 so that it divides exactly by 7?
  30. 30.What is the smallest number you must take away from 101 so that it divides exactly by 12?
  31. 31.How many factors does 34 have?
  32. 32.What is the smallest number you must take away from 349 so that it divides exactly by 3?
  33. 33.Which of these numbers divides exactly by 3? (a) 9490 (b) 9514 (c) 5411 (d) 8709
  34. 34.What is the smallest number you must add to 641 so that it divides exactly by 11?
  35. 35.What is the smallest number you must take away from 401 so that it divides exactly by 4?
  36. 36.What is the smallest number you must take away from 701 so that it divides exactly by 9?
  37. 37.Which of these numbers divides exactly by 4? (a) 3103 (b) 3384 (c) 6614 (d) 5601
  38. 38.How many factors does 45 have?
  39. 39.What is the smallest number you must add to 357 so that it divides exactly by 9?
  40. 40.How many factors does 85 have?

Answer key

  1. 7764
  2. 3
  3. 3
  4. 9180
  5. 1
  6. 8
  7. 5
  8. 1899
  9. 2
  10. 2
  11. 1
  12. 1
  13. 4
  14. 3
  15. 3780
  16. 8828
  17. 4
  18. 10
  19. 3008
  20. 5
  21. 4
  22. 4
  23. 3
  24. 8
  25. 5
  26. 1
  27. 3
  28. 4
  29. 5
  30. 5
  31. 4
  32. 1
  33. 8709
  34. 8
  35. 1
  36. 8
  37. 3384
  38. 6
  39. 3
  40. 4

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