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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 89 · 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 take away from 492 so that it divides exactly by 13?
  2. 2.What is the smallest number you must take away from 528 so that it divides exactly by 13?
  3. 3.What is the smallest number you must add to 578 so that it divides exactly by 4?
  4. 4.What is the smallest number you must take away from 947 so that it divides exactly by 6?
  5. 5.How many factors does 77 have?
  6. 6.Which of these numbers divides exactly by 9? (a) 1765 (b) 1827 (c) 7897 (d) 9836
  7. 7.What is the smallest number you must add to 566 so that it divides exactly by 6?
  8. 8.What is the smallest number you must add to 723 so that it divides exactly by 7?
  9. 9.Which of these numbers divides exactly by 4? (a) 4578 (b) 2119 (c) 8281 (d) 7676
  10. 10.Which of these numbers divides exactly by 8? (a) 1742 (b) 9015 (c) 6467 (d) 1400
  11. 11.What is the smallest number you must add to 164 so that it divides exactly by 7?
  12. 12.What is the smallest number you must take away from 509 so that it divides exactly by 7?
  13. 13.What is the smallest number you must take away from 407 so that it divides exactly by 3?
  14. 14.Which of these numbers divides exactly by 8? (a) 4226 (b) 1605 (c) 3292 (d) 4856
  15. 15.What is the smallest number you must add to 212 so that it divides exactly by 6?
  16. 16.How many factors does 37 have?
  17. 17.How many factors does 63 have?
  18. 18.How many factors does 16 have?
  19. 19.Which of these numbers divides exactly by 8? (a) 2659 (b) 1001 (c) 8769 (d) 9312
  20. 20.What is the smallest number you must take away from 326 so that it divides exactly by 12?
  21. 21.How many factors does 20 have?
  22. 22.What is the smallest number you must add to 829 so that it divides exactly by 6?
  23. 23.How many factors does 67 have?
  24. 24.How many factors does 91 have?
  25. 25.What is the smallest number you must add to 953 so that it divides exactly by 11?
  26. 26.How many factors does 33 have?
  27. 27.How many factors does 62 have?
  28. 28.How many factors does 86 have?
  29. 29.What is the smallest number you must take away from 136 so that it divides exactly by 11?
  30. 30.What is the smallest number you must take away from 738 so that it divides exactly by 8?
  31. 31.How many factors does 55 have?
  32. 32.What is the smallest number you must add to 545 so that it divides exactly by 4?
  33. 33.How many factors does 90 have?
  34. 34.What is the smallest number you must add to 553 so that it divides exactly by 8?
  35. 35.What is the smallest number you must add to 701 so that it divides exactly by 6?
  36. 36.Which of these numbers divides exactly by 3? (a) 6690 (b) 4820 (c) 4673 (d) 5273
  37. 37.What is the smallest number you must add to 251 so that it divides exactly by 7?
  38. 38.How many factors does 57 have?
  39. 39.How many factors does 47 have?
  40. 40.Which of these numbers divides exactly by 11? (a) 7820 (b) 8886 (c) 1662 (d) 1826

Answer key

  1. 11
  2. 8
  3. 2
  4. 5
  5. 4
  6. 1827
  7. 4
  8. 5
  9. 7676
  10. 1400
  11. 4
  12. 5
  13. 2
  14. 4856
  15. 4
  16. 2
  17. 6
  18. 5
  19. 9312
  20. 2
  21. 6
  22. 5
  23. 2
  24. 4
  25. 4
  26. 4
  27. 4
  28. 4
  29. 4
  30. 2
  31. 4
  32. 3
  33. 12
  34. 7
  35. 1
  36. 6690
  37. 1
  38. 4
  39. 2
  40. 1826

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