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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 201 · 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 62 have?
  2. 2.Which of these numbers divides exactly by 11? (a) 7927 (b) 1391 (c) 2508 (d) 9113
  3. 3.What is the smallest number you must take away from 339 so that it divides exactly by 4?
  4. 4.Which of these numbers divides exactly by 3? (a) 2542 (b) 7846 (c) 4800 (d) 1477
  5. 5.What is the smallest number you must take away from 135 so that it divides exactly by 7?
  6. 6.What is the smallest number you must take away from 652 so that it divides exactly by 9?
  7. 7.How many factors does 92 have?
  8. 8.What is the smallest number you must add to 195 so that it divides exactly by 7?
  9. 9.Which of these numbers divides exactly by 6? (a) 5864 (b) 3617 (c) 4259 (d) 6672
  10. 10.How many factors does 86 have?
  11. 11.What is the smallest number you must take away from 558 so that it divides exactly by 11?
  12. 12.Which of these numbers divides exactly by 4? (a) 8528 (b) 5486 (c) 4293 (d) 2189
  13. 13.How many factors does 83 have?
  14. 14.Which of these numbers divides exactly by 8? (a) 3371 (b) 8890 (c) 1367 (d) 6384
  15. 15.What is the smallest number you must add to 178 so that it divides exactly by 3?
  16. 16.What is the smallest number you must add to 785 so that it divides exactly by 13?
  17. 17.What is the smallest number you must add to 168 so that it divides exactly by 13?
  18. 18.Which of these numbers divides exactly by 6? (a) 9745 (b) 9414 (c) 9975 (d) 4773
  19. 19.How many factors does 96 have?
  20. 20.How many factors does 97 have?
  21. 21.What is the smallest number you must add to 302 so that it divides exactly by 8?
  22. 22.What is the smallest number you must add to 268 so that it divides exactly by 11?
  23. 23.What is the smallest number you must take away from 761 so that it divides exactly by 12?
  24. 24.What is the smallest number you must take away from 541 so that it divides exactly by 3?
  25. 25.What is the smallest number you must add to 820 so that it divides exactly by 3?
  26. 26.What is the smallest number you must take away from 929 so that it divides exactly by 8?
  27. 27.How many factors does 12 have?
  28. 28.What is the smallest number you must take away from 493 so that it divides exactly by 9?
  29. 29.What is the smallest number you must add to 972 so that it divides exactly by 8?
  30. 30.What is the smallest number you must take away from 565 so that it divides exactly by 13?
  31. 31.What is the smallest number you must add to 177 so that it divides exactly by 12?
  32. 32.What is the smallest number you must take away from 103 so that it divides exactly by 13?
  33. 33.What is the smallest number you must add to 753 so that it divides exactly by 7?
  34. 34.What is the smallest number you must add to 487 so that it divides exactly by 11?
  35. 35.How many factors does 57 have?
  36. 36.How many factors does 54 have?
  37. 37.What is the smallest number you must add to 870 so that it divides exactly by 9?
  38. 38.What is the smallest number you must add to 950 so that it divides exactly by 9?
  39. 39.How many factors does 26 have?
  40. 40.What is the smallest number you must take away from 214 so that it divides exactly by 9?

Answer key

  1. 4
  2. 2508
  3. 3
  4. 4800
  5. 2
  6. 4
  7. 6
  8. 1
  9. 6672
  10. 4
  11. 8
  12. 8528
  13. 2
  14. 6384
  15. 2
  16. 8
  17. 1
  18. 9414
  19. 12
  20. 2
  21. 2
  22. 7
  23. 5
  24. 1
  25. 2
  26. 1
  27. 6
  28. 7
  29. 4
  30. 6
  31. 3
  32. 12
  33. 3
  34. 8
  35. 4
  36. 8
  37. 3
  38. 4
  39. 4
  40. 7

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