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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 168 · 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 211 so that it divides exactly by 8?
  2. 2.What is the smallest number you must add to 370 so that it divides exactly by 6?
  3. 3.What is the smallest number you must add to 140 so that it divides exactly by 3?
  4. 4.What is the smallest number you must add to 716 so that it divides exactly by 3?
  5. 5.What is the smallest number you must add to 457 so that it divides exactly by 3?
  6. 6.What is the smallest number you must take away from 986 so that it divides exactly by 9?
  7. 7.How many factors does 97 have?
  8. 8.What is the smallest number you must add to 730 so that it divides exactly by 3?
  9. 9.What is the smallest number you must add to 645 so that it divides exactly by 6?
  10. 10.What is the smallest number you must add to 626 so that it divides exactly by 6?
  11. 11.What is the smallest number you must take away from 885 so that it divides exactly by 12?
  12. 12.How many factors does 56 have?
  13. 13.What is the smallest number you must take away from 308 so that it divides exactly by 9?
  14. 14.What is the smallest number you must add to 869 so that it divides exactly by 8?
  15. 15.How many factors does 29 have?
  16. 16.What is the smallest number you must add to 142 so that it divides exactly by 11?
  17. 17.Which of these numbers divides exactly by 8? (a) 8460 (b) 8119 (c) 3583 (d) 1672
  18. 18.How many factors does 16 have?
  19. 19.How many factors does 41 have?
  20. 20.What is the smallest number you must take away from 843 so that it divides exactly by 4?
  21. 21.How many factors does 32 have?
  22. 22.What is the smallest number you must add to 729 so that it divides exactly by 7?
  23. 23.What is the smallest number you must add to 919 so that it divides exactly by 7?
  24. 24.What is the smallest number you must take away from 832 so that it divides exactly by 12?
  25. 25.What is the smallest number you must add to 487 so that it divides exactly by 8?
  26. 26.What is the smallest number you must take away from 113 so that it divides exactly by 12?
  27. 27.What is the smallest number you must add to 192 so that it divides exactly by 13?
  28. 28.What is the smallest number you must add to 978 so that it divides exactly by 12?
  29. 29.What is the smallest number you must take away from 231 so that it divides exactly by 4?
  30. 30.How many factors does 75 have?
  31. 31.How many factors does 28 have?
  32. 32.What is the smallest number you must take away from 412 so that it divides exactly by 3?
  33. 33.What is the smallest number you must add to 265 so that it divides exactly by 13?
  34. 34.What is the smallest number you must add to 299 so that it divides exactly by 9?
  35. 35.Which of these numbers divides exactly by 4? (a) 3025 (b) 9906 (c) 8296 (d) 4725
  36. 36.What is the smallest number you must add to 118 so that it divides exactly by 8?
  37. 37.What is the smallest number you must add to 237 so that it divides exactly by 8?
  38. 38.How many factors does 24 have?
  39. 39.What is the smallest number you must add to 322 so that it divides exactly by 9?
  40. 40.What is the smallest number you must add to 211 so that it divides exactly by 8?

Answer key

  1. 3
  2. 2
  3. 1
  4. 1
  5. 2
  6. 5
  7. 2
  8. 2
  9. 3
  10. 4
  11. 9
  12. 8
  13. 2
  14. 3
  15. 2
  16. 1
  17. 1672
  18. 5
  19. 2
  20. 3
  21. 6
  22. 6
  23. 5
  24. 4
  25. 1
  26. 5
  27. 3
  28. 6
  29. 3
  30. 6
  31. 6
  32. 1
  33. 8
  34. 7
  35. 8296
  36. 2
  37. 3
  38. 8
  39. 2
  40. 5

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