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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 170 · 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 11? (a) 9859 (b) 7660 (c) 2451 (d) 7513
  2. 2.Which of these numbers divides exactly by 3? (a) 2890 (b) 4255 (c) 7527 (d) 4510
  3. 3.What is the smallest number you must add to 446 so that it divides exactly by 3?
  4. 4.Which of these numbers divides exactly by 4? (a) 9142 (b) 2629 (c) 3346 (d) 3044
  5. 5.What is the smallest number you must add to 409 so that it divides exactly by 7?
  6. 6.What is the smallest number you must add to 454 so that it divides exactly by 3?
  7. 7.How many factors does 27 have?
  8. 8.How many factors does 40 have?
  9. 9.What is the smallest number you must add to 690 so that it divides exactly by 4?
  10. 10.What is the smallest number you must add to 978 so that it divides exactly by 7?
  11. 11.What is the smallest number you must add to 362 so that it divides exactly by 9?
  12. 12.What is the smallest number you must take away from 660 so that it divides exactly by 7?
  13. 13.What is the smallest number you must take away from 977 so that it divides exactly by 4?
  14. 14.Which of these numbers divides exactly by 9? (a) 4513 (b) 9918 (c) 2570 (d) 1572
  15. 15.How many factors does 42 have?
  16. 16.Which of these numbers divides exactly by 4? (a) 6384 (b) 3410 (c) 3618 (d) 7621
  17. 17.How many factors does 32 have?
  18. 18.Which of these numbers divides exactly by 4? (a) 1977 (b) 5976 (c) 8986 (d) 2095
  19. 19.What is the smallest number you must add to 748 so that it divides exactly by 6?
  20. 20.Which of these numbers divides exactly by 3? (a) 8953 (b) 2528 (c) 3604 (d) 3609
  21. 21.How many factors does 20 have?
  22. 22.Which of these numbers divides exactly by 11? (a) 2164 (b) 6951 (c) 5599 (d) 3056
  23. 23.How many factors does 36 have?
  24. 24.How many factors does 90 have?
  25. 25.How many factors does 99 have?
  26. 26.Which of these numbers divides exactly by 3? (a) 7094 (b) 1000 (c) 2268 (d) 8876
  27. 27.Which of these numbers divides exactly by 8? (a) 5197 (b) 3940 (c) 1200 (d) 5349
  28. 28.What is the smallest number you must add to 133 so that it divides exactly by 12?
  29. 29.How many factors does 12 have?
  30. 30.How many factors does 64 have?
  31. 31.What is the smallest number you must add to 326 so that it divides exactly by 7?
  32. 32.Which of these numbers divides exactly by 8? (a) 9197 (b) 4152 (c) 3391 (d) 1186
  33. 33.How many factors does 21 have?
  34. 34.Which of these numbers divides exactly by 4? (a) 6765 (b) 5681 (c) 3893 (d) 7884
  35. 35.How many factors does 93 have?
  36. 36.Which of these numbers divides exactly by 3? (a) 8546 (b) 7540 (c) 4364 (d) 6213
  37. 37.How many factors does 60 have?
  38. 38.How many factors does 35 have?
  39. 39.What is the smallest number you must add to 935 so that it divides exactly by 9?
  40. 40.What is the smallest number you must take away from 872 so that it divides exactly by 7?

Answer key

  1. 7513
  2. 7527
  3. 1
  4. 3044
  5. 4
  6. 2
  7. 4
  8. 8
  9. 2
  10. 2
  11. 7
  12. 2
  13. 1
  14. 9918
  15. 8
  16. 6384
  17. 6
  18. 5976
  19. 2
  20. 3609
  21. 6
  22. 5599
  23. 9
  24. 12
  25. 6
  26. 2268
  27. 1200
  28. 11
  29. 6
  30. 7
  31. 3
  32. 4152
  33. 4
  34. 7884
  35. 4
  36. 6213
  37. 12
  38. 4
  39. 1
  40. 4

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