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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 321 · 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.Which of these numbers divides exactly by 3? (a) 1648 (b) 3858 (c) 3341 (d) 5713
  2. 2.What is the smallest number you must take away from 233 so that it divides exactly by 13?
  3. 3.What is the smallest number you must take away from 159 so that it divides exactly by 6?
  4. 4.What is the smallest number you must add to 321 so that it divides exactly by 13?
  5. 5.What is the smallest number you must take away from 828 so that it divides exactly by 13?
  6. 6.How many factors does 25 have?
  7. 7.What is the smallest number you must add to 556 so that it divides exactly by 6?
  8. 8.What is the smallest number you must take away from 885 so that it divides exactly by 4?
  9. 9.How many factors does 80 have?
  10. 10.How many factors does 98 have?
  11. 11.How many factors does 82 have?
  12. 12.What is the smallest number you must take away from 489 so that it divides exactly by 7?
  13. 13.How many factors does 83 have?
  14. 14.What is the smallest number you must add to 709 so that it divides exactly by 4?
  15. 15.What is the smallest number you must take away from 490 so that it divides exactly by 4?
  16. 16.Which of these numbers divides exactly by 4? (a) 1634 (b) 9395 (c) 4176 (d) 3426
  17. 17.Which of these numbers divides exactly by 6? (a) 6457 (b) 2623 (c) 5412 (d) 9340
  18. 18.How many factors does 29 have?
  19. 19.What is the smallest number you must add to 970 so that it divides exactly by 4?
  20. 20.What is the smallest number you must take away from 904 so that it divides exactly by 9?
  21. 21.Which of these numbers divides exactly by 11? (a) 4479 (b) 8834 (c) 6237 (d) 5547
  22. 22.How many factors does 43 have?
  23. 23.Which of these numbers divides exactly by 9? (a) 3192 (b) 2448 (c) 8102 (d) 7802
  24. 24.What is the smallest number you must take away from 374 so that it divides exactly by 7?
  25. 25.How many factors does 65 have?
  26. 26.How many factors does 66 have?
  27. 27.What is the smallest number you must take away from 974 so that it divides exactly by 8?
  28. 28.What is the smallest number you must add to 886 so that it divides exactly by 11?
  29. 29.How many factors does 17 have?
  30. 30.How many factors does 63 have?
  31. 31.How many factors does 30 have?
  32. 32.How many factors does 28 have?
  33. 33.How many factors does 92 have?
  34. 34.What is the smallest number you must take away from 365 so that it divides exactly by 13?
  35. 35.What is the smallest number you must add to 530 so that it divides exactly by 4?
  36. 36.Which of these numbers divides exactly by 3? (a) 4588 (b) 5870 (c) 1853 (d) 2244
  37. 37.What is the smallest number you must add to 650 so that it divides exactly by 3?
  38. 38.How many factors does 77 have?
  39. 39.How many factors does 78 have?
  40. 40.What is the smallest number you must add to 883 so that it divides exactly by 12?

Answer key

  1. 3858
  2. 12
  3. 3
  4. 4
  5. 9
  6. 3
  7. 2
  8. 1
  9. 10
  10. 6
  11. 4
  12. 6
  13. 2
  14. 3
  15. 2
  16. 4176
  17. 5412
  18. 2
  19. 2
  20. 4
  21. 6237
  22. 2
  23. 2448
  24. 3
  25. 4
  26. 8
  27. 6
  28. 5
  29. 2
  30. 6
  31. 8
  32. 6
  33. 6
  34. 1
  35. 2
  36. 2244
  37. 1
  38. 4
  39. 8
  40. 5

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