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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 166 · 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.How many factors does 74 have?
  2. 2.Which of these numbers divides exactly by 3? (a) 9987 (b) 5851 (c) 7843 (d) 7631
  3. 3.Which of these numbers divides exactly by 9? (a) 4293 (b) 4747 (c) 2671 (d) 2474
  4. 4.How many factors does 68 have?
  5. 5.Which of these numbers divides exactly by 8? (a) 7416 (b) 1542 (c) 7866 (d) 6618
  6. 6.What is the smallest number you must add to 998 so that it divides exactly by 3?
  7. 7.How many factors does 73 have?
  8. 8.Which of these numbers divides exactly by 3? (a) 7337 (b) 9937 (c) 1923 (d) 4162
  9. 9.What is the smallest number you must add to 651 so that it divides exactly by 4?
  10. 10.How many factors does 16 have?
  11. 11.What is the smallest number you must add to 302 so that it divides exactly by 6?
  12. 12.Which of these numbers divides exactly by 3? (a) 9374 (b) 7196 (c) 4323 (d) 7096
  13. 13.What is the smallest number you must add to 923 so that it divides exactly by 3?
  14. 14.What is the smallest number you must take away from 401 so that it divides exactly by 4?
  15. 15.Which of these numbers divides exactly by 11? (a) 3223 (b) 3104 (c) 8157 (d) 9206
  16. 16.How many factors does 43 have?
  17. 17.How many factors does 90 have?
  18. 18.What is the smallest number you must take away from 734 so that it divides exactly by 12?
  19. 19.Which of these numbers divides exactly by 4? (a) 5145 (b) 1557 (c) 9716 (d) 3927
  20. 20.What is the smallest number you must take away from 645 so that it divides exactly by 7?
  21. 21.How many factors does 78 have?
  22. 22.Which of these numbers divides exactly by 3? (a) 7483 (b) 4374 (c) 6815 (d) 3029
  23. 23.Which of these numbers divides exactly by 6? (a) 8797 (b) 1647 (c) 8556 (d) 8339
  24. 24.What is the smallest number you must add to 255 so that it divides exactly by 6?
  25. 25.How many factors does 28 have?
  26. 26.What is the smallest number you must take away from 259 so that it divides exactly by 12?
  27. 27.What is the smallest number you must take away from 957 so that it divides exactly by 13?
  28. 28.What is the smallest number you must take away from 697 so that it divides exactly by 11?
  29. 29.How many factors does 34 have?
  30. 30.How many factors does 49 have?
  31. 31.What is the smallest number you must take away from 144 so that it divides exactly by 11?
  32. 32.What is the smallest number you must take away from 733 so that it divides exactly by 12?
  33. 33.How many factors does 92 have?
  34. 34.How many factors does 13 have?
  35. 35.What is the smallest number you must add to 491 so that it divides exactly by 12?
  36. 36.What is the smallest number you must take away from 541 so that it divides exactly by 8?
  37. 37.How many factors does 48 have?
  38. 38.Which of these numbers divides exactly by 11? (a) 5122 (b) 7518 (c) 3126 (d) 2618
  39. 39.What is the smallest number you must take away from 411 so that it divides exactly by 9?
  40. 40.What is the smallest number you must add to 908 so that it divides exactly by 11?

Answer key

  1. 4
  2. 9987
  3. 4293
  4. 6
  5. 7416
  6. 1
  7. 2
  8. 1923
  9. 1
  10. 5
  11. 4
  12. 4323
  13. 1
  14. 1
  15. 3223
  16. 2
  17. 12
  18. 2
  19. 9716
  20. 1
  21. 8
  22. 4374
  23. 8556
  24. 3
  25. 6
  26. 7
  27. 8
  28. 4
  29. 4
  30. 3
  31. 1
  32. 1
  33. 6
  34. 2
  35. 1
  36. 5
  37. 10
  38. 2618
  39. 6
  40. 5

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