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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 16 · 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 74 have?
  2. 2.How many factors does 88 have?
  3. 3.What is the smallest number you must add to 201 so that it divides exactly by 7?
  4. 4.Which of these numbers divides exactly by 8? (a) 6212 (b) 7363 (c) 5312 (d) 3116
  5. 5.How many factors does 83 have?
  6. 6.Which of these numbers divides exactly by 9? (a) 3915 (b) 9833 (c) 7852 (d) 2462
  7. 7.How many factors does 27 have?
  8. 8.Which of these numbers divides exactly by 6? (a) 4151 (b) 1168 (c) 7525 (d) 3498
  9. 9.What is the smallest number you must add to 887 so that it divides exactly by 8?
  10. 10.What is the smallest number you must take away from 581 so that it divides exactly by 9?
  11. 11.Which of these numbers divides exactly by 6? (a) 4166 (b) 3030 (c) 7028 (d) 2839
  12. 12.How many factors does 97 have?
  13. 13.How many factors does 59 have?
  14. 14.How many factors does 41 have?
  15. 15.What is the smallest number you must take away from 426 so that it divides exactly by 12?
  16. 16.How many factors does 39 have?
  17. 17.What is the smallest number you must add to 155 so that it divides exactly by 4?
  18. 18.What is the smallest number you must take away from 515 so that it divides exactly by 11?
  19. 19.How many factors does 64 have?
  20. 20.How many factors does 21 have?
  21. 21.What is the smallest number you must take away from 265 so that it divides exactly by 11?
  22. 22.What is the smallest number you must take away from 875 so that it divides exactly by 11?
  23. 23.What is the smallest number you must take away from 463 so that it divides exactly by 13?
  24. 24.How many factors does 51 have?
  25. 25.How many factors does 16 have?
  26. 26.What is the smallest number you must add to 791 so that it divides exactly by 13?
  27. 27.How many factors does 52 have?
  28. 28.Which of these numbers divides exactly by 6? (a) 1323 (b) 9246 (c) 7043 (d) 2309
  29. 29.What is the smallest number you must add to 612 so that it divides exactly by 8?
  30. 30.How many factors does 95 have?
  31. 31.How many factors does 93 have?
  32. 32.What is the smallest number you must take away from 141 so that it divides exactly by 11?
  33. 33.Which of these numbers divides exactly by 8? (a) 1627 (b) 1888 (c) 1481 (d) 3317
  34. 34.What is the smallest number you must add to 997 so that it divides exactly by 12?
  35. 35.How many factors does 40 have?
  36. 36.What is the smallest number you must take away from 511 so that it divides exactly by 3?
  37. 37.How many factors does 33 have?
  38. 38.What is the smallest number you must take away from 326 so that it divides exactly by 7?
  39. 39.What is the smallest number you must add to 979 so that it divides exactly by 13?
  40. 40.How many factors does 46 have?

Answer key

  1. 4
  2. 8
  3. 2
  4. 5312
  5. 2
  6. 3915
  7. 4
  8. 3498
  9. 1
  10. 5
  11. 3030
  12. 2
  13. 2
  14. 2
  15. 6
  16. 4
  17. 1
  18. 9
  19. 7
  20. 4
  21. 1
  22. 6
  23. 8
  24. 4
  25. 5
  26. 2
  27. 6
  28. 9246
  29. 4
  30. 4
  31. 4
  32. 9
  33. 1888
  34. 11
  35. 8
  36. 1
  37. 4
  38. 4
  39. 9
  40. 4

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