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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 189 · 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 39 have?
  2. 2.Which of these numbers divides exactly by 6? (a) 5598 (b) 4940 (c) 5505 (d) 2599
  3. 3.Which of these numbers divides exactly by 11? (a) 5246 (b) 3220 (c) 7931 (d) 5428
  4. 4.Which of these numbers divides exactly by 9? (a) 1948 (b) 5386 (c) 3267 (d) 8291
  5. 5.What is the smallest number you must add to 859 so that it divides exactly by 11?
  6. 6.Which of these numbers divides exactly by 4? (a) 3429 (b) 8455 (c) 4299 (d) 8336
  7. 7.Which of these numbers divides exactly by 4? (a) 2217 (b) 2386 (c) 2182 (d) 8352
  8. 8.Which of these numbers divides exactly by 9? (a) 3075 (b) 9857 (c) 2151 (d) 1813
  9. 9.Which of these numbers divides exactly by 8? (a) 1081 (b) 1329 (c) 8584 (d) 7636
  10. 10.What is the smallest number you must add to 325 so that it divides exactly by 3?
  11. 11.How many factors does 17 have?
  12. 12.What is the smallest number you must take away from 691 so that it divides exactly by 12?
  13. 13.What is the smallest number you must take away from 107 so that it divides exactly by 13?
  14. 14.What is the smallest number you must add to 578 so that it divides exactly by 3?
  15. 15.How many factors does 49 have?
  16. 16.What is the smallest number you must take away from 142 so that it divides exactly by 12?
  17. 17.Which of these numbers divides exactly by 3? (a) 8356 (b) 6370 (c) 2497 (d) 1497
  18. 18.What is the smallest number you must take away from 799 so that it divides exactly by 6?
  19. 19.What is the smallest number you must take away from 489 so that it divides exactly by 12?
  20. 20.How many factors does 35 have?
  21. 21.Which of these numbers divides exactly by 3? (a) 9457 (b) 1682 (c) 8149 (d) 2658
  22. 22.How many factors does 83 have?
  23. 23.What is the smallest number you must take away from 274 so that it divides exactly by 6?
  24. 24.How many factors does 78 have?
  25. 25.How many factors does 80 have?
  26. 26.Which of these numbers divides exactly by 9? (a) 2976 (b) 8464 (c) 7659 (d) 1869
  27. 27.What is the smallest number you must add to 421 so that it divides exactly by 9?
  28. 28.How many factors does 82 have?
  29. 29.How many factors does 58 have?
  30. 30.How many factors does 70 have?
  31. 31.What is the smallest number you must take away from 903 so that it divides exactly by 6?
  32. 32.Which of these numbers divides exactly by 8? (a) 3312 (b) 5546 (c) 7299 (d) 8865
  33. 33.What is the smallest number you must add to 417 so that it divides exactly by 6?
  34. 34.Which of these numbers divides exactly by 6? (a) 9535 (b) 9107 (c) 7794 (d) 3502
  35. 35.How many factors does 73 have?
  36. 36.What is the smallest number you must add to 482 so that it divides exactly by 9?
  37. 37.What is the smallest number you must add to 708 so that it divides exactly by 13?
  38. 38.How many factors does 93 have?
  39. 39.How many factors does 46 have?
  40. 40.How many factors does 36 have?

Answer key

  1. 4
  2. 5598
  3. 7931
  4. 3267
  5. 10
  6. 8336
  7. 8352
  8. 2151
  9. 8584
  10. 2
  11. 2
  12. 7
  13. 3
  14. 1
  15. 3
  16. 10
  17. 1497
  18. 1
  19. 9
  20. 4
  21. 2658
  22. 2
  23. 4
  24. 8
  25. 10
  26. 7659
  27. 2
  28. 4
  29. 4
  30. 8
  31. 3
  32. 3312
  33. 3
  34. 7794
  35. 2
  36. 4
  37. 7
  38. 4
  39. 4
  40. 9

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