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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 113 · 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 4? (a) 8867 (b) 1020 (c) 4905 (d) 9671
  2. 2.Which of these numbers divides exactly by 6? (a) 2540 (b) 2553 (c) 9098 (d) 3660
  3. 3.What is the smallest number you must take away from 656 so that it divides exactly by 9?
  4. 4.Which of these numbers divides exactly by 9? (a) 4059 (b) 7053 (c) 7211 (d) 7400
  5. 5.How many factors does 51 have?
  6. 6.Which of these numbers divides exactly by 3? (a) 6413 (b) 5408 (c) 3134 (d) 8511
  7. 7.What is the smallest number you must add to 282 so that it divides exactly by 7?
  8. 8.Which of these numbers divides exactly by 3? (a) 4978 (b) 1168 (c) 8748 (d) 9338
  9. 9.How many factors does 22 have?
  10. 10.Which of these numbers divides exactly by 8? (a) 2141 (b) 9001 (c) 4808 (d) 7919
  11. 11.What is the smallest number you must take away from 184 so that it divides exactly by 13?
  12. 12.Which of these numbers divides exactly by 8? (a) 9604 (b) 4541 (c) 3600 (d) 9569
  13. 13.Which of these numbers divides exactly by 11? (a) 8850 (b) 3977 (c) 4312 (d) 3957
  14. 14.How many factors does 84 have?
  15. 15.What is the smallest number you must take away from 327 so that it divides exactly by 4?
  16. 16.How many factors does 97 have?
  17. 17.How many factors does 40 have?
  18. 18.How many factors does 58 have?
  19. 19.What is the smallest number you must add to 563 so that it divides exactly by 12?
  20. 20.How many factors does 45 have?
  21. 21.How many factors does 12 have?
  22. 22.What is the smallest number you must add to 558 so that it divides exactly by 11?
  23. 23.How many factors does 60 have?
  24. 24.How many factors does 19 have?
  25. 25.Which of these numbers divides exactly by 4? (a) 8335 (b) 2585 (c) 8449 (d) 3800
  26. 26.Which of these numbers divides exactly by 3? (a) 8887 (b) 1402 (c) 2819 (d) 8835
  27. 27.How many factors does 88 have?
  28. 28.What is the smallest number you must take away from 267 so that it divides exactly by 7?
  29. 29.How many factors does 87 have?
  30. 30.What is the smallest number you must take away from 771 so that it divides exactly by 8?
  31. 31.How many factors does 49 have?
  32. 32.What is the smallest number you must add to 341 so that it divides exactly by 4?
  33. 33.What is the smallest number you must add to 173 so that it divides exactly by 12?
  34. 34.How many factors does 38 have?
  35. 35.What is the smallest number you must take away from 151 so that it divides exactly by 7?
  36. 36.Which of these numbers divides exactly by 9? (a) 6138 (b) 5781 (c) 2531 (d) 1317
  37. 37.Which of these numbers divides exactly by 6? (a) 1251 (b) 9295 (c) 8105 (d) 9138
  38. 38.What is the smallest number you must take away from 435 so that it divides exactly by 7?
  39. 39.How many factors does 34 have?
  40. 40.What is the smallest number you must add to 311 so that it divides exactly by 3?

Answer key

  1. 1020
  2. 3660
  3. 8
  4. 4059
  5. 4
  6. 8511
  7. 5
  8. 8748
  9. 4
  10. 4808
  11. 2
  12. 3600
  13. 4312
  14. 12
  15. 3
  16. 2
  17. 8
  18. 4
  19. 1
  20. 6
  21. 6
  22. 3
  23. 12
  24. 2
  25. 3800
  26. 8835
  27. 8
  28. 1
  29. 4
  30. 3
  31. 3
  32. 3
  33. 7
  34. 4
  35. 4
  36. 6138
  37. 9138
  38. 1
  39. 4
  40. 1

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