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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 199 · 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 91 have?
  2. 2.What is the smallest number you must add to 249 so that it divides exactly by 7?
  3. 3.Which of these numbers divides exactly by 6? (a) 3537 (b) 6693 (c) 7254 (d) 6459
  4. 4.What is the smallest number you must add to 881 so that it divides exactly by 9?
  5. 5.What is the smallest number you must take away from 347 so that it divides exactly by 13?
  6. 6.How many factors does 17 have?
  7. 7.Which of these numbers divides exactly by 4? (a) 2313 (b) 8529 (c) 4366 (d) 1396
  8. 8.How many factors does 95 have?
  9. 9.How many factors does 58 have?
  10. 10.How many factors does 92 have?
  11. 11.How many factors does 25 have?
  12. 12.How many factors does 66 have?
  13. 13.How many factors does 65 have?
  14. 14.How many factors does 19 have?
  15. 15.How many factors does 82 have?
  16. 16.Which of these numbers divides exactly by 3? (a) 2560 (b) 2020 (c) 3089 (d) 4854
  17. 17.How many factors does 41 have?
  18. 18.How many factors does 98 have?
  19. 19.What is the smallest number you must add to 646 so that it divides exactly by 3?
  20. 20.Which of these numbers divides exactly by 9? (a) 2939 (b) 9813 (c) 4779 (d) 4256
  21. 21.What is the smallest number you must take away from 271 so that it divides exactly by 6?
  22. 22.How many factors does 43 have?
  23. 23.What is the smallest number you must take away from 397 so that it divides exactly by 6?
  24. 24.What is the smallest number you must take away from 596 so that it divides exactly by 11?
  25. 25.What is the smallest number you must add to 692 so that it divides exactly by 8?
  26. 26.What is the smallest number you must add to 625 so that it divides exactly by 9?
  27. 27.What is the smallest number you must take away from 283 so that it divides exactly by 12?
  28. 28.What is the smallest number you must take away from 509 so that it divides exactly by 9?
  29. 29.Which of these numbers divides exactly by 3? (a) 6667 (b) 7067 (c) 5387 (d) 3126
  30. 30.What is the smallest number you must take away from 821 so that it divides exactly by 4?
  31. 31.What is the smallest number you must add to 186 so that it divides exactly by 8?
  32. 32.Which of these numbers divides exactly by 6? (a) 7078 (b) 8149 (c) 2847 (d) 7620
  33. 33.Which of these numbers divides exactly by 6? (a) 3535 (b) 3090 (c) 2755 (d) 6567
  34. 34.What is the smallest number you must take away from 488 so that it divides exactly by 7?
  35. 35.What is the smallest number you must add to 573 so that it divides exactly by 13?
  36. 36.How many factors does 68 have?
  37. 37.Which of these numbers divides exactly by 11? (a) 8028 (b) 3604 (c) 3058 (d) 6928
  38. 38.How many factors does 78 have?
  39. 39.What is the smallest number you must add to 786 so that it divides exactly by 12?
  40. 40.What is the smallest number you must take away from 508 so that it divides exactly by 8?

Answer key

  1. 4
  2. 3
  3. 7254
  4. 1
  5. 9
  6. 2
  7. 1396
  8. 4
  9. 4
  10. 6
  11. 3
  12. 8
  13. 4
  14. 2
  15. 4
  16. 4854
  17. 2
  18. 6
  19. 2
  20. 4779
  21. 1
  22. 2
  23. 1
  24. 2
  25. 4
  26. 5
  27. 7
  28. 5
  29. 3126
  30. 1
  31. 6
  32. 7620
  33. 3090
  34. 5
  35. 12
  36. 6
  37. 3058
  38. 8
  39. 6
  40. 4

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