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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 144 · 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 980 so that it divides exactly by 8?
  2. 2.How many factors does 34 have?
  3. 3.How many factors does 98 have?
  4. 4.How many factors does 36 have?
  5. 5.What is the smallest number you must take away from 100 so that it divides exactly by 6?
  6. 6.What is the smallest number you must add to 259 so that it divides exactly by 3?
  7. 7.What is the smallest number you must add to 595 so that it divides exactly by 6?
  8. 8.What is the smallest number you must take away from 966 so that it divides exactly by 11?
  9. 9.What is the smallest number you must take away from 931 so that it divides exactly by 6?
  10. 10.Which of these numbers divides exactly by 8? (a) 1779 (b) 1458 (c) 9568 (d) 3891
  11. 11.What is the smallest number you must take away from 135 so that it divides exactly by 4?
  12. 12.What is the smallest number you must add to 611 so that it divides exactly by 3?
  13. 13.Which of these numbers divides exactly by 11? (a) 7036 (b) 2607 (c) 6976 (d) 5249
  14. 14.What is the smallest number you must add to 379 so that it divides exactly by 3?
  15. 15.What is the smallest number you must add to 762 so that it divides exactly by 9?
  16. 16.What is the smallest number you must add to 447 so that it divides exactly by 13?
  17. 17.How many factors does 75 have?
  18. 18.What is the smallest number you must add to 164 so that it divides exactly by 3?
  19. 19.How many factors does 27 have?
  20. 20.Which of these numbers divides exactly by 8? (a) 6345 (b) 1883 (c) 1588 (d) 3552
  21. 21.Which of these numbers divides exactly by 4? (a) 9422 (b) 6572 (c) 1571 (d) 6613
  22. 22.What is the smallest number you must add to 349 so that it divides exactly by 11?
  23. 23.What is the smallest number you must add to 278 so that it divides exactly by 13?
  24. 24.How many factors does 38 have?
  25. 25.How many factors does 100 have?
  26. 26.What is the smallest number you must add to 487 so that it divides exactly by 12?
  27. 27.Which of these numbers divides exactly by 8? (a) 3252 (b) 7112 (c) 2291 (d) 1108
  28. 28.How many factors does 62 have?
  29. 29.What is the smallest number you must take away from 446 so that it divides exactly by 12?
  30. 30.How many factors does 93 have?
  31. 31.Which of these numbers divides exactly by 4? (a) 4431 (b) 4693 (c) 7908 (d) 4282
  32. 32.Which of these numbers divides exactly by 4? (a) 9020 (b) 4481 (c) 6711 (d) 3561
  33. 33.What is the smallest number you must add to 885 so that it divides exactly by 9?
  34. 34.How many factors does 43 have?
  35. 35.What is the smallest number you must take away from 280 so that it divides exactly by 3?
  36. 36.How many factors does 20 have?
  37. 37.Which of these numbers divides exactly by 4? (a) 7044 (b) 4065 (c) 9929 (d) 2043
  38. 38.How many factors does 66 have?
  39. 39.What is the smallest number you must add to 180 so that it divides exactly by 7?
  40. 40.Which of these numbers divides exactly by 3? (a) 7922 (b) 1507 (c) 5281 (d) 8703

Answer key

  1. 4
  2. 4
  3. 6
  4. 9
  5. 4
  6. 2
  7. 5
  8. 9
  9. 1
  10. 9568
  11. 3
  12. 1
  13. 2607
  14. 2
  15. 3
  16. 8
  17. 6
  18. 1
  19. 4
  20. 3552
  21. 6572
  22. 3
  23. 8
  24. 4
  25. 9
  26. 5
  27. 7112
  28. 4
  29. 2
  30. 4
  31. 7908
  32. 9020
  33. 6
  34. 2
  35. 1
  36. 6
  37. 7044
  38. 8
  39. 2
  40. 8703

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