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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 118 · 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 28 have?
  2. 2.What is the smallest number you must add to 817 so that it divides exactly by 9?
  3. 3.How many factors does 27 have?
  4. 4.What is the smallest number you must take away from 263 so that it divides exactly by 6?
  5. 5.Which of these numbers divides exactly by 3? (a) 7712 (b) 8171 (c) 8382 (d) 8647
  6. 6.Which of these numbers divides exactly by 6? (a) 3156 (b) 6759 (c) 7227 (d) 4570
  7. 7.How many factors does 82 have?
  8. 8.What is the smallest number you must add to 523 so that it divides exactly by 7?
  9. 9.What is the smallest number you must take away from 544 so that it divides exactly by 3?
  10. 10.Which of these numbers divides exactly by 9? (a) 7712 (b) 8118 (c) 8628 (d) 2209
  11. 11.Which of these numbers divides exactly by 9? (a) 2547 (b) 2418 (c) 2119 (d) 8945
  12. 12.What is the smallest number you must add to 415 so that it divides exactly by 3?
  13. 13.What is the smallest number you must take away from 291 so that it divides exactly by 4?
  14. 14.What is the smallest number you must take away from 542 so that it divides exactly by 6?
  15. 15.Which of these numbers divides exactly by 6? (a) 3245 (b) 9043 (c) 4562 (d) 6978
  16. 16.What is the smallest number you must add to 831 so that it divides exactly by 8?
  17. 17.How many factors does 88 have?
  18. 18.What is the smallest number you must take away from 986 so that it divides exactly by 13?
  19. 19.How many factors does 13 have?
  20. 20.What is the smallest number you must add to 496 so that it divides exactly by 7?
  21. 21.How many factors does 23 have?
  22. 22.What is the smallest number you must add to 103 so that it divides exactly by 3?
  23. 23.How many factors does 97 have?
  24. 24.What is the smallest number you must add to 238 so that it divides exactly by 12?
  25. 25.What is the smallest number you must take away from 612 so that it divides exactly by 7?
  26. 26.Which of these numbers divides exactly by 8? (a) 7524 (b) 3671 (c) 5735 (d) 2312
  27. 27.How many factors does 92 have?
  28. 28.How many factors does 26 have?
  29. 29.How many factors does 32 have?
  30. 30.Which of these numbers divides exactly by 9? (a) 3868 (b) 5780 (c) 6339 (d) 9603
  31. 31.What is the smallest number you must take away from 812 so that it divides exactly by 3?
  32. 32.Which of these numbers divides exactly by 4? (a) 2209 (b) 2981 (c) 4136 (d) 5783
  33. 33.Which of these numbers divides exactly by 11? (a) 9149 (b) 9220 (c) 2354 (d) 3604
  34. 34.What is the smallest number you must take away from 109 so that it divides exactly by 9?
  35. 35.How many factors does 36 have?
  36. 36.How many factors does 58 have?
  37. 37.What is the smallest number you must add to 286 so that it divides exactly by 3?
  38. 38.How many factors does 47 have?
  39. 39.How many factors does 80 have?
  40. 40.How many factors does 78 have?

Answer key

  1. 6
  2. 2
  3. 4
  4. 5
  5. 8382
  6. 3156
  7. 4
  8. 2
  9. 1
  10. 8118
  11. 2547
  12. 2
  13. 3
  14. 2
  15. 6978
  16. 1
  17. 8
  18. 11
  19. 2
  20. 1
  21. 2
  22. 2
  23. 2
  24. 2
  25. 3
  26. 2312
  27. 6
  28. 4
  29. 6
  30. 9603
  31. 2
  32. 4136
  33. 2354
  34. 1
  35. 9
  36. 4
  37. 2
  38. 2
  39. 10
  40. 8

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