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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 106 · 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 249 so that it divides exactly by 7?
  2. 2.What is the smallest number you must take away from 620 so that it divides exactly by 11?
  3. 3.What is the smallest number you must add to 790 so that it divides exactly by 8?
  4. 4.How many factors does 20 have?
  5. 5.Which of these numbers divides exactly by 6? (a) 1520 (b) 4903 (c) 1512 (d) 1931
  6. 6.How many factors does 84 have?
  7. 7.What is the smallest number you must take away from 355 so that it divides exactly by 9?
  8. 8.Which of these numbers divides exactly by 3? (a) 8864 (b) 7754 (c) 2464 (d) 2721
  9. 9.What is the smallest number you must take away from 790 so that it divides exactly by 12?
  10. 10.What is the smallest number you must take away from 409 so that it divides exactly by 4?
  11. 11.Which of these numbers divides exactly by 9? (a) 5388 (b) 8523 (c) 8056 (d) 3819
  12. 12.How many factors does 46 have?
  13. 13.How many factors does 76 have?
  14. 14.How many factors does 13 have?
  15. 15.What is the smallest number you must take away from 952 so that it divides exactly by 13?
  16. 16.How many factors does 64 have?
  17. 17.What is the smallest number you must take away from 469 so that it divides exactly by 13?
  18. 18.What is the smallest number you must add to 868 so that it divides exactly by 13?
  19. 19.Which of these numbers divides exactly by 4? (a) 5269 (b) 6347 (c) 8363 (d) 3588
  20. 20.How many factors does 50 have?
  21. 21.What is the smallest number you must add to 202 so that it divides exactly by 9?
  22. 22.Which of these numbers divides exactly by 3? (a) 7455 (b) 5618 (c) 7049 (d) 8239
  23. 23.Which of these numbers divides exactly by 3? (a) 6790 (b) 1251 (c) 8018 (d) 9338
  24. 24.What is the smallest number you must add to 660 so that it divides exactly by 13?
  25. 25.How many factors does 27 have?
  26. 26.What is the smallest number you must add to 849 so that it divides exactly by 13?
  27. 27.What is the smallest number you must take away from 413 so that it divides exactly by 9?
  28. 28.What is the smallest number you must add to 261 so that it divides exactly by 13?
  29. 29.What is the smallest number you must add to 493 so that it divides exactly by 12?
  30. 30.What is the smallest number you must take away from 851 so that it divides exactly by 11?
  31. 31.What is the smallest number you must add to 968 so that it divides exactly by 7?
  32. 32.What is the smallest number you must take away from 766 so that it divides exactly by 3?
  33. 33.How many factors does 15 have?
  34. 34.Which of these numbers divides exactly by 11? (a) 9592 (b) 5040 (c) 1228 (d) 9552
  35. 35.How many factors does 51 have?
  36. 36.What is the smallest number you must take away from 354 so that it divides exactly by 4?
  37. 37.How many factors does 83 have?
  38. 38.What is the smallest number you must take away from 519 so that it divides exactly by 11?
  39. 39.How many factors does 56 have?
  40. 40.Which of these numbers divides exactly by 11? (a) 1514 (b) 3174 (c) 9000 (d) 2222

Answer key

  1. 4
  2. 4
  3. 2
  4. 6
  5. 1512
  6. 12
  7. 4
  8. 2721
  9. 10
  10. 1
  11. 8523
  12. 4
  13. 6
  14. 2
  15. 3
  16. 7
  17. 1
  18. 3
  19. 3588
  20. 6
  21. 5
  22. 7455
  23. 1251
  24. 3
  25. 4
  26. 9
  27. 8
  28. 12
  29. 11
  30. 4
  31. 5
  32. 1
  33. 4
  34. 9592
  35. 4
  36. 2
  37. 2
  38. 2
  39. 8
  40. 2222

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