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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 225 · 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 348 so that it divides exactly by 9?
  2. 2.What is the smallest number you must take away from 133 so that it divides exactly by 8?
  3. 3.What is the smallest number you must take away from 462 so that it divides exactly by 4?
  4. 4.What is the smallest number you must add to 394 so that it divides exactly by 6?
  5. 5.How many factors does 47 have?
  6. 6.Which of these numbers divides exactly by 8? (a) 8914 (b) 7288 (c) 6803 (d) 3131
  7. 7.What is the smallest number you must take away from 659 so that it divides exactly by 4?
  8. 8.How many factors does 29 have?
  9. 9.How many factors does 25 have?
  10. 10.Which of these numbers divides exactly by 8? (a) 1234 (b) 2657 (c) 9443 (d) 4920
  11. 11.Which of these numbers divides exactly by 11? (a) 6793 (b) 1375 (c) 1445 (d) 8665
  12. 12.What is the smallest number you must add to 185 so that it divides exactly by 7?
  13. 13.Which of these numbers divides exactly by 6? (a) 8426 (b) 3913 (c) 2711 (d) 7992
  14. 14.What is the smallest number you must add to 892 so that it divides exactly by 9?
  15. 15.What is the smallest number you must take away from 942 so that it divides exactly by 13?
  16. 16.What is the smallest number you must add to 454 so that it divides exactly by 7?
  17. 17.How many factors does 63 have?
  18. 18.What is the smallest number you must take away from 200 so that it divides exactly by 13?
  19. 19.What is the smallest number you must take away from 889 so that it divides exactly by 8?
  20. 20.What is the smallest number you must take away from 430 so that it divides exactly by 7?
  21. 21.What is the smallest number you must take away from 320 so that it divides exactly by 13?
  22. 22.What is the smallest number you must take away from 210 so that it divides exactly by 13?
  23. 23.Which of these numbers divides exactly by 8? (a) 1418 (b) 8894 (c) 5528 (d) 2938
  24. 24.What is the smallest number you must take away from 573 so that it divides exactly by 13?
  25. 25.What is the smallest number you must add to 237 so that it divides exactly by 9?
  26. 26.Which of these numbers divides exactly by 3? (a) 7127 (b) 2557 (c) 8313 (d) 1736
  27. 27.What is the smallest number you must add to 722 so that it divides exactly by 9?
  28. 28.What is the smallest number you must take away from 695 so that it divides exactly by 13?
  29. 29.What is the smallest number you must take away from 250 so that it divides exactly by 3?
  30. 30.Which of these numbers divides exactly by 11? (a) 3818 (b) 1805 (c) 1378 (d) 6336
  31. 31.What is the smallest number you must take away from 498 so that it divides exactly by 8?
  32. 32.How many factors does 50 have?
  33. 33.What is the smallest number you must take away from 275 so that it divides exactly by 4?
  34. 34.What is the smallest number you must add to 480 so that it divides exactly by 11?
  35. 35.How many factors does 22 have?
  36. 36.What is the smallest number you must add to 843 so that it divides exactly by 6?
  37. 37.What is the smallest number you must take away from 780 so that it divides exactly by 9?
  38. 38.What is the smallest number you must add to 201 so that it divides exactly by 8?
  39. 39.What is the smallest number you must take away from 469 so that it divides exactly by 12?
  40. 40.What is the smallest number you must take away from 106 so that it divides exactly by 6?

Answer key

  1. 3
  2. 5
  3. 2
  4. 2
  5. 2
  6. 7288
  7. 3
  8. 2
  9. 3
  10. 4920
  11. 1375
  12. 4
  13. 7992
  14. 8
  15. 6
  16. 1
  17. 6
  18. 5
  19. 1
  20. 3
  21. 8
  22. 2
  23. 5528
  24. 1
  25. 6
  26. 8313
  27. 7
  28. 6
  29. 1
  30. 6336
  31. 2
  32. 6
  33. 3
  34. 4
  35. 4
  36. 3
  37. 6
  38. 7
  39. 1
  40. 4

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