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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 217 · 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 939 so that it divides exactly by 6?
  2. 2.What is the smallest number you must add to 973 so that it divides exactly by 9?
  3. 3.What is the smallest number you must take away from 307 so that it divides exactly by 13?
  4. 4.What is the smallest number you must add to 951 so that it divides exactly by 11?
  5. 5.What is the smallest number you must take away from 253 so that it divides exactly by 6?
  6. 6.How many factors does 77 have?
  7. 7.What is the smallest number you must take away from 894 so that it divides exactly by 13?
  8. 8.What is the smallest number you must take away from 123 so that it divides exactly by 8?
  9. 9.How many factors does 37 have?
  10. 10.What is the smallest number you must take away from 822 so that it divides exactly by 12?
  11. 11.How many factors does 17 have?
  12. 12.Which of these numbers divides exactly by 11? (a) 4370 (b) 4115 (c) 7667 (d) 1131
  13. 13.What is the smallest number you must take away from 666 so that it divides exactly by 11?
  14. 14.How many factors does 75 have?
  15. 15.How many factors does 100 have?
  16. 16.What is the smallest number you must add to 256 so that it divides exactly by 11?
  17. 17.What is the smallest number you must add to 465 so that it divides exactly by 4?
  18. 18.What is the smallest number you must add to 766 so that it divides exactly by 12?
  19. 19.What is the smallest number you must add to 683 so that it divides exactly by 3?
  20. 20.Which of these numbers divides exactly by 6? (a) 4574 (b) 7398 (c) 9645 (d) 2228
  21. 21.What is the smallest number you must add to 579 so that it divides exactly by 6?
  22. 22.What is the smallest number you must add to 622 so that it divides exactly by 6?
  23. 23.What is the smallest number you must add to 878 so that it divides exactly by 8?
  24. 24.Which of these numbers divides exactly by 8? (a) 9703 (b) 6360 (c) 2164 (d) 4530
  25. 25.How many factors does 30 have?
  26. 26.What is the smallest number you must add to 174 so that it divides exactly by 4?
  27. 27.What is the smallest number you must add to 197 so that it divides exactly by 7?
  28. 28.How many factors does 31 have?
  29. 29.What is the smallest number you must take away from 985 so that it divides exactly by 13?
  30. 30.How many factors does 73 have?
  31. 31.What is the smallest number you must take away from 245 so that it divides exactly by 9?
  32. 32.Which of these numbers divides exactly by 11? (a) 3821 (b) 7170 (c) 2492 (d) 2805
  33. 33.What is the smallest number you must add to 576 so that it divides exactly by 13?
  34. 34.How many factors does 95 have?
  35. 35.What is the smallest number you must add to 211 so that it divides exactly by 8?
  36. 36.How many factors does 55 have?
  37. 37.What is the smallest number you must add to 275 so that it divides exactly by 4?
  38. 38.Which of these numbers divides exactly by 4? (a) 1124 (b) 3746 (c) 6037 (d) 4853
  39. 39.How many factors does 70 have?
  40. 40.What is the smallest number you must add to 193 so that it divides exactly by 12?

Answer key

  1. 3
  2. 8
  3. 8
  4. 6
  5. 1
  6. 4
  7. 10
  8. 3
  9. 2
  10. 6
  11. 2
  12. 7667
  13. 6
  14. 6
  15. 9
  16. 8
  17. 3
  18. 2
  19. 1
  20. 7398
  21. 3
  22. 2
  23. 2
  24. 6360
  25. 8
  26. 2
  27. 6
  28. 2
  29. 10
  30. 2
  31. 2
  32. 2805
  33. 9
  34. 4
  35. 5
  36. 4
  37. 1
  38. 1124
  39. 8
  40. 11

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