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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 208 · 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.Which of these numbers divides exactly by 3? (a) 5771 (b) 2269 (c) 1203 (d) 1084
  2. 2.How many factors does 67 have?
  3. 3.How many factors does 29 have?
  4. 4.What is the smallest number you must add to 251 so that it divides exactly by 12?
  5. 5.Which of these numbers divides exactly by 8? (a) 9498 (b) 9991 (c) 8107 (d) 2080
  6. 6.Which of these numbers divides exactly by 4? (a) 1961 (b) 7682 (c) 2038 (d) 4444
  7. 7.How many factors does 98 have?
  8. 8.How many factors does 26 have?
  9. 9.What is the smallest number you must add to 764 so that it divides exactly by 3?
  10. 10.What is the smallest number you must take away from 584 so that it divides exactly by 12?
  11. 11.How many factors does 34 have?
  12. 12.Which of these numbers divides exactly by 8? (a) 3374 (b) 8448 (c) 4862 (d) 1774
  13. 13.What is the smallest number you must add to 869 so that it divides exactly by 9?
  14. 14.Which of these numbers divides exactly by 3? (a) 3797 (b) 2995 (c) 5549 (d) 3156
  15. 15.Which of these numbers divides exactly by 3? (a) 5629 (b) 1952 (c) 2652 (d) 2866
  16. 16.How many factors does 89 have?
  17. 17.How many factors does 12 have?
  18. 18.What is the smallest number you must take away from 669 so that it divides exactly by 7?
  19. 19.What is the smallest number you must add to 622 so that it divides exactly by 4?
  20. 20.Which of these numbers divides exactly by 9? (a) 6979 (b) 3141 (c) 9490 (d) 6026
  21. 21.What is the smallest number you must add to 780 so that it divides exactly by 11?
  22. 22.How many factors does 93 have?
  23. 23.What is the smallest number you must take away from 376 so that it divides exactly by 3?
  24. 24.What is the smallest number you must add to 529 so that it divides exactly by 6?
  25. 25.What is the smallest number you must take away from 627 so that it divides exactly by 9?
  26. 26.How many factors does 21 have?
  27. 27.What is the smallest number you must add to 314 so that it divides exactly by 3?
  28. 28.How many factors does 15 have?
  29. 29.How many factors does 55 have?
  30. 30.Which of these numbers divides exactly by 3? (a) 5848 (b) 8664 (c) 5386 (d) 1684
  31. 31.What is the smallest number you must add to 834 so that it divides exactly by 13?
  32. 32.What is the smallest number you must add to 592 so that it divides exactly by 3?
  33. 33.Which of these numbers divides exactly by 3? (a) 2738 (b) 4531 (c) 9285 (d) 6760
  34. 34.Which of these numbers divides exactly by 9? (a) 1420 (b) 5274 (c) 2342 (d) 8270
  35. 35.What is the smallest number you must take away from 107 so that it divides exactly by 7?
  36. 36.How many factors does 51 have?
  37. 37.How many factors does 31 have?
  38. 38.What is the smallest number you must take away from 792 so that it divides exactly by 13?
  39. 39.What is the smallest number you must take away from 703 so that it divides exactly by 9?
  40. 40.Which of these numbers divides exactly by 6? (a) 8511 (b) 4151 (c) 8196 (d) 3123

Answer key

  1. 1203
  2. 2
  3. 2
  4. 1
  5. 2080
  6. 4444
  7. 6
  8. 4
  9. 1
  10. 8
  11. 4
  12. 8448
  13. 4
  14. 3156
  15. 2652
  16. 2
  17. 6
  18. 4
  19. 2
  20. 3141
  21. 1
  22. 4
  23. 1
  24. 5
  25. 6
  26. 4
  27. 1
  28. 4
  29. 4
  30. 8664
  31. 11
  32. 2
  33. 9285
  34. 5274
  35. 2
  36. 4
  37. 2
  38. 12
  39. 1
  40. 8196

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