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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 261 · 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 265 so that it divides exactly by 11?
  2. 2.How many factors does 77 have?
  3. 3.How many factors does 26 have?
  4. 4.Which of these numbers divides exactly by 4? (a) 2597 (b) 5206 (c) 6647 (d) 1440
  5. 5.What is the smallest number you must add to 998 so that it divides exactly by 8?
  6. 6.Which of these numbers divides exactly by 9? (a) 8326 (b) 6617 (c) 5724 (d) 1369
  7. 7.What is the smallest number you must take away from 382 so that it divides exactly by 8?
  8. 8.How many factors does 60 have?
  9. 9.What is the smallest number you must take away from 311 so that it divides exactly by 13?
  10. 10.How many factors does 89 have?
  11. 11.What is the smallest number you must take away from 299 so that it divides exactly by 4?
  12. 12.What is the smallest number you must take away from 479 so that it divides exactly by 7?
  13. 13.What is the smallest number you must add to 876 so that it divides exactly by 13?
  14. 14.What is the smallest number you must add to 136 so that it divides exactly by 12?
  15. 15.How many factors does 24 have?
  16. 16.Which of these numbers divides exactly by 11? (a) 4569 (b) 4743 (c) 7721 (d) 5379
  17. 17.What is the smallest number you must add to 565 so that it divides exactly by 11?
  18. 18.What is the smallest number you must add to 414 so that it divides exactly by 4?
  19. 19.How many factors does 98 have?
  20. 20.What is the smallest number you must take away from 818 so that it divides exactly by 9?
  21. 21.How many factors does 18 have?
  22. 22.How many factors does 45 have?
  23. 23.What is the smallest number you must add to 880 so that it divides exactly by 6?
  24. 24.What is the smallest number you must add to 490 so that it divides exactly by 11?
  25. 25.What is the smallest number you must take away from 446 so that it divides exactly by 9?
  26. 26.What is the smallest number you must add to 486 so that it divides exactly by 8?
  27. 27.Which of these numbers divides exactly by 4? (a) 3630 (b) 2518 (c) 9460 (d) 4121
  28. 28.How many factors does 90 have?
  29. 29.What is the smallest number you must take away from 740 so that it divides exactly by 13?
  30. 30.What is the smallest number you must take away from 462 so that it divides exactly by 13?
  31. 31.What is the smallest number you must add to 790 so that it divides exactly by 8?
  32. 32.How many factors does 47 have?
  33. 33.What is the smallest number you must add to 305 so that it divides exactly by 12?
  34. 34.What is the smallest number you must take away from 281 so that it divides exactly by 12?
  35. 35.Which of these numbers divides exactly by 11? (a) 3672 (b) 1669 (c) 3175 (d) 2618
  36. 36.How many factors does 91 have?
  37. 37.What is the smallest number you must add to 825 so that it divides exactly by 4?
  38. 38.What is the smallest number you must add to 291 so that it divides exactly by 13?
  39. 39.How many factors does 13 have?
  40. 40.What is the smallest number you must add to 834 so that it divides exactly by 12?

Answer key

  1. 10
  2. 4
  3. 4
  4. 1440
  5. 2
  6. 5724
  7. 6
  8. 12
  9. 12
  10. 2
  11. 3
  12. 3
  13. 8
  14. 8
  15. 8
  16. 5379
  17. 7
  18. 2
  19. 6
  20. 8
  21. 6
  22. 6
  23. 2
  24. 5
  25. 5
  26. 2
  27. 9460
  28. 12
  29. 12
  30. 7
  31. 2
  32. 2
  33. 7
  34. 5
  35. 2618
  36. 4
  37. 3
  38. 8
  39. 2
  40. 6

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