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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 221 · 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 654 so that it divides exactly by 8?
  2. 2.How many factors does 96 have?
  3. 3.What is the smallest number you must add to 363 so that it divides exactly by 13?
  4. 4.How many factors does 88 have?
  5. 5.How many factors does 57 have?
  6. 6.How many factors does 32 have?
  7. 7.What is the smallest number you must add to 666 so that it divides exactly by 8?
  8. 8.Which of these numbers divides exactly by 8? (a) 2267 (b) 3176 (c) 8547 (d) 5012
  9. 9.How many factors does 27 have?
  10. 10.What is the smallest number you must take away from 281 so that it divides exactly by 4?
  11. 11.What is the smallest number you must add to 206 so that it divides exactly by 4?
  12. 12.What is the smallest number you must add to 321 so that it divides exactly by 12?
  13. 13.How many factors does 67 have?
  14. 14.What is the smallest number you must take away from 137 so that it divides exactly by 7?
  15. 15.How many factors does 30 have?
  16. 16.How many factors does 39 have?
  17. 17.What is the smallest number you must take away from 359 so that it divides exactly by 9?
  18. 18.Which of these numbers divides exactly by 3? (a) 2790 (b) 1598 (c) 5168 (d) 8354
  19. 19.What is the smallest number you must take away from 449 so that it divides exactly by 7?
  20. 20.How many factors does 72 have?
  21. 21.How many factors does 37 have?
  22. 22.What is the smallest number you must add to 163 so that it divides exactly by 4?
  23. 23.What is the smallest number you must add to 302 so that it divides exactly by 11?
  24. 24.What is the smallest number you must take away from 905 so that it divides exactly by 8?
  25. 25.Which of these numbers divides exactly by 9? (a) 3823 (b) 3595 (c) 4125 (d) 6768
  26. 26.How many factors does 99 have?
  27. 27.What is the smallest number you must take away from 215 so that it divides exactly by 9?
  28. 28.What is the smallest number you must take away from 129 so that it divides exactly by 11?
  29. 29.What is the smallest number you must take away from 244 so that it divides exactly by 6?
  30. 30.Which of these numbers divides exactly by 4? (a) 2279 (b) 4048 (c) 6545 (d) 2105
  31. 31.Which of these numbers divides exactly by 11? (a) 6316 (b) 4101 (c) 1452 (d) 8391
  32. 32.What is the smallest number you must take away from 563 so that it divides exactly by 7?
  33. 33.What is the smallest number you must add to 985 so that it divides exactly by 6?
  34. 34.What is the smallest number you must add to 248 so that it divides exactly by 6?
  35. 35.Which of these numbers divides exactly by 3? (a) 9565 (b) 2211 (c) 3310 (d) 9521
  36. 36.What is the smallest number you must add to 202 so that it divides exactly by 4?
  37. 37.What is the smallest number you must add to 789 so that it divides exactly by 12?
  38. 38.What is the smallest number you must add to 980 so that it divides exactly by 8?
  39. 39.What is the smallest number you must add to 777 so that it divides exactly by 8?
  40. 40.How many factors does 62 have?

Answer key

  1. 6
  2. 12
  3. 1
  4. 8
  5. 4
  6. 6
  7. 6
  8. 3176
  9. 4
  10. 1
  11. 2
  12. 3
  13. 2
  14. 4
  15. 8
  16. 4
  17. 8
  18. 2790
  19. 1
  20. 12
  21. 2
  22. 1
  23. 6
  24. 1
  25. 6768
  26. 6
  27. 8
  28. 8
  29. 4
  30. 4048
  31. 1452
  32. 3
  33. 5
  34. 4
  35. 2211
  36. 2
  37. 3
  38. 4
  39. 7
  40. 4

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