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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 62 · 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 62 have?
  2. 2.How many factors does 65 have?
  3. 3.How many factors does 36 have?
  4. 4.How many factors does 75 have?
  5. 5.What is the smallest number you must add to 294 so that it divides exactly by 12?
  6. 6.What is the smallest number you must take away from 611 so that it divides exactly by 11?
  7. 7.What is the smallest number you must add to 724 so that it divides exactly by 13?
  8. 8.How many factors does 38 have?
  9. 9.Which of these numbers divides exactly by 3? (a) 1979 (b) 9384 (c) 1031 (d) 5192
  10. 10.Which of these numbers divides exactly by 3? (a) 1355 (b) 2444 (c) 5773 (d) 7737
  11. 11.What is the smallest number you must take away from 590 so that it divides exactly by 12?
  12. 12.What is the smallest number you must take away from 465 so that it divides exactly by 13?
  13. 13.How many factors does 70 have?
  14. 14.What is the smallest number you must take away from 452 so that it divides exactly by 3?
  15. 15.How many factors does 68 have?
  16. 16.Which of these numbers divides exactly by 9? (a) 6249 (b) 1405 (c) 3186 (d) 7024
  17. 17.What is the smallest number you must take away from 344 so that it divides exactly by 11?
  18. 18.Which of these numbers divides exactly by 4? (a) 8567 (b) 3580 (c) 3510 (d) 3706
  19. 19.What is the smallest number you must take away from 836 so that it divides exactly by 13?
  20. 20.How many factors does 52 have?
  21. 21.How many factors does 79 have?
  22. 22.How many factors does 66 have?
  23. 23.What is the smallest number you must add to 199 so that it divides exactly by 8?
  24. 24.What is the smallest number you must add to 294 so that it divides exactly by 11?
  25. 25.What is the smallest number you must take away from 820 so that it divides exactly by 7?
  26. 26.What is the smallest number you must add to 946 so that it divides exactly by 9?
  27. 27.How many factors does 83 have?
  28. 28.What is the smallest number you must take away from 304 so that it divides exactly by 3?
  29. 29.What is the smallest number you must add to 972 so that it divides exactly by 8?
  30. 30.What is the smallest number you must take away from 142 so that it divides exactly by 3?
  31. 31.How many factors does 61 have?
  32. 32.Which of these numbers divides exactly by 11? (a) 8732 (b) 6317 (c) 4148 (d) 3355
  33. 33.What is the smallest number you must take away from 547 so that it divides exactly by 13?
  34. 34.How many factors does 23 have?
  35. 35.What is the smallest number you must take away from 707 so that it divides exactly by 13?
  36. 36.What is the smallest number you must add to 243 so that it divides exactly by 6?
  37. 37.How many factors does 15 have?
  38. 38.Which of these numbers divides exactly by 3? (a) 2064 (b) 3503 (c) 4271 (d) 1385
  39. 39.How many factors does 39 have?
  40. 40.Which of these numbers divides exactly by 6? (a) 3610 (b) 3881 (c) 3332 (d) 3030

Answer key

  1. 4
  2. 4
  3. 9
  4. 6
  5. 6
  6. 6
  7. 4
  8. 4
  9. 9384
  10. 7737
  11. 2
  12. 10
  13. 8
  14. 2
  15. 6
  16. 3186
  17. 3
  18. 3580
  19. 4
  20. 6
  21. 2
  22. 8
  23. 1
  24. 3
  25. 1
  26. 8
  27. 2
  28. 1
  29. 4
  30. 1
  31. 2
  32. 3355
  33. 1
  34. 2
  35. 5
  36. 3
  37. 4
  38. 2064
  39. 4
  40. 3030

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