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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 11 · 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 94 have?
  2. 2.What is the smallest number you must take away from 133 so that it divides exactly by 13?
  3. 3.What is the smallest number you must add to 604 so that it divides exactly by 6?
  4. 4.What is the smallest number you must take away from 961 so that it divides exactly by 7?
  5. 5.What is the smallest number you must take away from 590 so that it divides exactly by 3?
  6. 6.How many factors does 70 have?
  7. 7.What is the smallest number you must take away from 940 so that it divides exactly by 3?
  8. 8.What is the smallest number you must take away from 362 so that it divides exactly by 6?
  9. 9.What is the smallest number you must add to 244 so that it divides exactly by 13?
  10. 10.What is the smallest number you must take away from 750 so that it divides exactly by 4?
  11. 11.How many factors does 87 have?
  12. 12.What is the smallest number you must add to 436 so that it divides exactly by 3?
  13. 13.What is the smallest number you must add to 785 so that it divides exactly by 6?
  14. 14.What is the smallest number you must take away from 485 so that it divides exactly by 12?
  15. 15.How many factors does 84 have?
  16. 16.How many factors does 79 have?
  17. 17.How many factors does 50 have?
  18. 18.How many factors does 20 have?
  19. 19.Which of these numbers divides exactly by 8? (a) 9456 (b) 3484 (c) 3181 (d) 6493
  20. 20.What is the smallest number you must take away from 139 so that it divides exactly by 12?
  21. 21.Which of these numbers divides exactly by 3? (a) 8298 (b) 3473 (c) 2144 (d) 2282
  22. 22.Which of these numbers divides exactly by 3? (a) 9476 (b) 2055 (c) 1631 (d) 4565
  23. 23.What is the smallest number you must take away from 148 so that it divides exactly by 6?
  24. 24.What is the smallest number you must add to 125 so that it divides exactly by 6?
  25. 25.How many factors does 71 have?
  26. 26.How many factors does 88 have?
  27. 27.What is the smallest number you must add to 257 so that it divides exactly by 13?
  28. 28.How many factors does 31 have?
  29. 29.How many factors does 30 have?
  30. 30.What is the smallest number you must take away from 132 so that it divides exactly by 8?
  31. 31.How many factors does 56 have?
  32. 32.What is the smallest number you must take away from 857 so that it divides exactly by 4?
  33. 33.What is the smallest number you must take away from 223 so that it divides exactly by 7?
  34. 34.How many factors does 41 have?
  35. 35.What is the smallest number you must add to 935 so that it divides exactly by 13?
  36. 36.What is the smallest number you must add to 907 so that it divides exactly by 3?
  37. 37.What is the smallest number you must add to 896 so that it divides exactly by 6?
  38. 38.What is the smallest number you must add to 103 so that it divides exactly by 11?
  39. 39.How many factors does 60 have?
  40. 40.How many factors does 44 have?

Answer key

  1. 4
  2. 3
  3. 2
  4. 2
  5. 2
  6. 8
  7. 1
  8. 2
  9. 3
  10. 2
  11. 4
  12. 2
  13. 1
  14. 5
  15. 12
  16. 2
  17. 6
  18. 6
  19. 9456
  20. 7
  21. 8298
  22. 2055
  23. 4
  24. 1
  25. 2
  26. 8
  27. 3
  28. 2
  29. 8
  30. 4
  31. 8
  32. 1
  33. 6
  34. 2
  35. 1
  36. 2
  37. 4
  38. 7
  39. 12
  40. 6

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