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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 248 · 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 301 so that it divides exactly by 3?
  2. 2.What is the smallest number you must add to 658 so that it divides exactly by 4?
  3. 3.How many factors does 52 have?
  4. 4.What is the smallest number you must take away from 323 so that it divides exactly by 11?
  5. 5.What is the smallest number you must add to 376 so that it divides exactly by 12?
  6. 6.What is the smallest number you must take away from 543 so that it divides exactly by 8?
  7. 7.How many factors does 86 have?
  8. 8.How many factors does 98 have?
  9. 9.How many factors does 12 have?
  10. 10.What is the smallest number you must take away from 749 so that it divides exactly by 11?
  11. 11.How many factors does 51 have?
  12. 12.What is the smallest number you must add to 393 so that it divides exactly by 9?
  13. 13.How many factors does 21 have?
  14. 14.Which of these numbers divides exactly by 3? (a) 7026 (b) 5345 (c) 8494 (d) 4540
  15. 15.What is the smallest number you must take away from 576 so that it divides exactly by 13?
  16. 16.What is the smallest number you must add to 687 so that it divides exactly by 9?
  17. 17.How many factors does 58 have?
  18. 18.What is the smallest number you must add to 332 so that it divides exactly by 9?
  19. 19.What is the smallest number you must add to 567 so that it divides exactly by 4?
  20. 20.Which of these numbers divides exactly by 9? (a) 3193 (b) 2747 (c) 8487 (d) 4268
  21. 21.What is the smallest number you must take away from 167 so that it divides exactly by 11?
  22. 22.What is the smallest number you must add to 541 so that it divides exactly by 13?
  23. 23.Which of these numbers divides exactly by 4? (a) 4463 (b) 9456 (c) 4818 (d) 4551
  24. 24.How many factors does 90 have?
  25. 25.How many factors does 26 have?
  26. 26.What is the smallest number you must add to 878 so that it divides exactly by 8?
  27. 27.Which of these numbers divides exactly by 4? (a) 3699 (b) 1807 (c) 3368 (d) 4861
  28. 28.How many factors does 78 have?
  29. 29.What is the smallest number you must add to 746 so that it divides exactly by 4?
  30. 30.What is the smallest number you must add to 506 so that it divides exactly by 13?
  31. 31.What is the smallest number you must take away from 311 so that it divides exactly by 13?
  32. 32.What is the smallest number you must take away from 847 so that it divides exactly by 4?
  33. 33.What is the smallest number you must take away from 190 so that it divides exactly by 13?
  34. 34.How many factors does 41 have?
  35. 35.What is the smallest number you must add to 881 so that it divides exactly by 7?
  36. 36.What is the smallest number you must take away from 559 so that it divides exactly by 8?
  37. 37.Which of these numbers divides exactly by 8? (a) 5997 (b) 1291 (c) 6628 (d) 2184
  38. 38.Which of these numbers divides exactly by 9? (a) 4514 (b) 4204 (c) 8411 (d) 6363
  39. 39.How many factors does 72 have?
  40. 40.What is the smallest number you must take away from 984 so that it divides exactly by 13?

Answer key

  1. 1
  2. 2
  3. 6
  4. 4
  5. 8
  6. 7
  7. 4
  8. 6
  9. 6
  10. 1
  11. 4
  12. 3
  13. 4
  14. 7026
  15. 4
  16. 6
  17. 4
  18. 1
  19. 1
  20. 8487
  21. 2
  22. 5
  23. 9456
  24. 12
  25. 4
  26. 2
  27. 3368
  28. 8
  29. 2
  30. 1
  31. 12
  32. 3
  33. 8
  34. 2
  35. 1
  36. 7
  37. 2184
  38. 6363
  39. 12
  40. 9

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