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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 313 · 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 add to 103 so that it divides exactly by 13?
  2. 2.How many factors does 59 have?
  3. 3.Which of these numbers divides exactly by 9? (a) 7974 (b) 4201 (c) 1367 (d) 2309
  4. 4.How many factors does 60 have?
  5. 5.What is the smallest number you must take away from 619 so that it divides exactly by 9?
  6. 6.How many factors does 79 have?
  7. 7.How many factors does 40 have?
  8. 8.How many factors does 13 have?
  9. 9.How many factors does 74 have?
  10. 10.How many factors does 98 have?
  11. 11.What is the smallest number you must take away from 605 so that it divides exactly by 7?
  12. 12.What is the smallest number you must take away from 960 so that it divides exactly by 11?
  13. 13.How many factors does 93 have?
  14. 14.Which of these numbers divides exactly by 6? (a) 2572 (b) 4051 (c) 2879 (d) 3744
  15. 15.What is the smallest number you must add to 915 so that it divides exactly by 6?
  16. 16.What is the smallest number you must take away from 155 so that it divides exactly by 11?
  17. 17.What is the smallest number you must take away from 607 so that it divides exactly by 11?
  18. 18.What is the smallest number you must add to 959 so that it divides exactly by 8?
  19. 19.How many factors does 39 have?
  20. 20.How many factors does 67 have?
  21. 21.How many factors does 18 have?
  22. 22.How many factors does 94 have?
  23. 23.What is the smallest number you must add to 704 so that it divides exactly by 9?
  24. 24.How many factors does 49 have?
  25. 25.Which of these numbers divides exactly by 4? (a) 7443 (b) 8316 (c) 1019 (d) 2667
  26. 26.What is the smallest number you must add to 241 so that it divides exactly by 6?
  27. 27.How many factors does 73 have?
  28. 28.What is the smallest number you must add to 610 so that it divides exactly by 4?
  29. 29.Which of these numbers divides exactly by 6? (a) 5531 (b) 3150 (c) 8689 (d) 2745
  30. 30.What is the smallest number you must add to 432 so that it divides exactly by 13?
  31. 31.What is the smallest number you must take away from 831 so that it divides exactly by 12?
  32. 32.What is the smallest number you must take away from 224 so that it divides exactly by 11?
  33. 33.Which of these numbers divides exactly by 6? (a) 3364 (b) 5269 (c) 5128 (d) 1632
  34. 34.How many factors does 45 have?
  35. 35.What is the smallest number you must add to 510 so that it divides exactly by 8?
  36. 36.How many factors does 92 have?
  37. 37.How many factors does 15 have?
  38. 38.How many factors does 86 have?
  39. 39.What is the smallest number you must take away from 736 so that it divides exactly by 12?
  40. 40.What is the smallest number you must take away from 301 so that it divides exactly by 6?

Answer key

  1. 1
  2. 2
  3. 7974
  4. 12
  5. 7
  6. 2
  7. 8
  8. 2
  9. 4
  10. 6
  11. 3
  12. 3
  13. 4
  14. 3744
  15. 3
  16. 1
  17. 2
  18. 1
  19. 4
  20. 2
  21. 6
  22. 4
  23. 7
  24. 3
  25. 8316
  26. 5
  27. 2
  28. 2
  29. 3150
  30. 10
  31. 3
  32. 4
  33. 1632
  34. 6
  35. 2
  36. 6
  37. 4
  38. 4
  39. 4
  40. 1

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