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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 60 · 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 add to 392 so that it divides exactly by 6?
  2. 2.How many factors does 56 have?
  3. 3.Which of these numbers divides exactly by 4? (a) 6022 (b) 1668 (c) 2443 (d) 6411
  4. 4.How many factors does 35 have?
  5. 5.What is the smallest number you must take away from 730 so that it divides exactly by 9?
  6. 6.What is the smallest number you must add to 873 so that it divides exactly by 12?
  7. 7.How many factors does 34 have?
  8. 8.Which of these numbers divides exactly by 4? (a) 5044 (b) 8077 (c) 6835 (d) 3202
  9. 9.What is the smallest number you must add to 376 so that it divides exactly by 9?
  10. 10.How many factors does 33 have?
  11. 11.What is the smallest number you must take away from 340 so that it divides exactly by 13?
  12. 12.What is the smallest number you must add to 126 so that it divides exactly by 12?
  13. 13.How many factors does 31 have?
  14. 14.How many factors does 39 have?
  15. 15.How many factors does 47 have?
  16. 16.What is the smallest number you must add to 274 so that it divides exactly by 9?
  17. 17.What is the smallest number you must add to 294 so that it divides exactly by 4?
  18. 18.What is the smallest number you must add to 671 so that it divides exactly by 3?
  19. 19.What is the smallest number you must add to 490 so that it divides exactly by 4?
  20. 20.What is the smallest number you must take away from 225 so that it divides exactly by 7?
  21. 21.Which of these numbers divides exactly by 4? (a) 8842 (b) 5598 (c) 8303 (d) 1440
  22. 22.What is the smallest number you must take away from 908 so that it divides exactly by 3?
  23. 23.How many factors does 17 have?
  24. 24.What is the smallest number you must take away from 666 so that it divides exactly by 12?
  25. 25.Which of these numbers divides exactly by 8? (a) 1065 (b) 2830 (c) 3616 (d) 5597
  26. 26.What is the smallest number you must add to 256 so that it divides exactly by 3?
  27. 27.How many factors does 40 have?
  28. 28.What is the smallest number you must add to 952 so that it divides exactly by 6?
  29. 29.Which of these numbers divides exactly by 11? (a) 8343 (b) 7052 (c) 7246 (d) 8998
  30. 30.Which of these numbers divides exactly by 4? (a) 4686 (b) 4828 (c) 3771 (d) 4659
  31. 31.Which of these numbers divides exactly by 8? (a) 7174 (b) 3559 (c) 8392 (d) 7183
  32. 32.How many factors does 98 have?
  33. 33.What is the smallest number you must take away from 633 so that it divides exactly by 7?
  34. 34.How many factors does 62 have?
  35. 35.How many factors does 50 have?
  36. 36.How many factors does 15 have?
  37. 37.What is the smallest number you must add to 940 so that it divides exactly by 8?
  38. 38.What is the smallest number you must take away from 194 so that it divides exactly by 3?
  39. 39.What is the smallest number you must take away from 642 so that it divides exactly by 8?
  40. 40.What is the smallest number you must add to 667 so that it divides exactly by 12?

Answer key

  1. 4
  2. 8
  3. 1668
  4. 4
  5. 1
  6. 3
  7. 4
  8. 5044
  9. 2
  10. 4
  11. 2
  12. 6
  13. 2
  14. 4
  15. 2
  16. 5
  17. 2
  18. 1
  19. 2
  20. 1
  21. 1440
  22. 2
  23. 2
  24. 6
  25. 3616
  26. 2
  27. 8
  28. 2
  29. 8998
  30. 4828
  31. 8392
  32. 6
  33. 3
  34. 4
  35. 6
  36. 4
  37. 4
  38. 2
  39. 2
  40. 5

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