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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 232 · 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 152 so that it divides exactly by 13?
  2. 2.What is the smallest number you must add to 890 so that it divides exactly by 3?
  3. 3.What is the smallest number you must add to 109 so that it divides exactly by 7?
  4. 4.What is the smallest number you must add to 183 so that it divides exactly by 12?
  5. 5.What is the smallest number you must add to 343 so that it divides exactly by 13?
  6. 6.How many factors does 46 have?
  7. 7.Which of these numbers divides exactly by 4? (a) 7363 (b) 5013 (c) 5944 (d) 3337
  8. 8.What is the smallest number you must take away from 559 so that it divides exactly by 7?
  9. 9.How many factors does 95 have?
  10. 10.What is the smallest number you must add to 802 so that it divides exactly by 4?
  11. 11.How many factors does 15 have?
  12. 12.What is the smallest number you must add to 402 so that it divides exactly by 7?
  13. 13.How many factors does 49 have?
  14. 14.What is the smallest number you must add to 268 so that it divides exactly by 13?
  15. 15.Which of these numbers divides exactly by 3? (a) 7950 (b) 5276 (c) 9286 (d) 4303
  16. 16.What is the smallest number you must take away from 979 so that it divides exactly by 4?
  17. 17.How many factors does 94 have?
  18. 18.Which of these numbers divides exactly by 3? (a) 8351 (b) 5006 (c) 6519 (d) 4859
  19. 19.How many factors does 43 have?
  20. 20.What is the smallest number you must take away from 569 so that it divides exactly by 3?
  21. 21.Which of these numbers divides exactly by 6? (a) 7789 (b) 2499 (c) 1650 (d) 2464
  22. 22.What is the smallest number you must add to 262 so that it divides exactly by 3?
  23. 23.What is the smallest number you must take away from 472 so that it divides exactly by 13?
  24. 24.How many factors does 32 have?
  25. 25.What is the smallest number you must add to 260 so that it divides exactly by 7?
  26. 26.How many factors does 24 have?
  27. 27.How many factors does 30 have?
  28. 28.Which of these numbers divides exactly by 11? (a) 4913 (b) 3781 (c) 2805 (d) 3457
  29. 29.What is the smallest number you must take away from 449 so that it divides exactly by 6?
  30. 30.Which of these numbers divides exactly by 6? (a) 5638 (b) 1181 (c) 1374 (d) 7807
  31. 31.What is the smallest number you must take away from 961 so that it divides exactly by 4?
  32. 32.What is the smallest number you must take away from 742 so that it divides exactly by 8?
  33. 33.Which of these numbers divides exactly by 4? (a) 2518 (b) 3172 (c) 7495 (d) 9430
  34. 34.What is the smallest number you must add to 267 so that it divides exactly by 4?
  35. 35.What is the smallest number you must add to 931 so that it divides exactly by 12?
  36. 36.What is the smallest number you must add to 462 so that it divides exactly by 4?
  37. 37.What is the smallest number you must add to 812 so that it divides exactly by 3?
  38. 38.What is the smallest number you must add to 786 so that it divides exactly by 12?
  39. 39.What is the smallest number you must take away from 531 so that it divides exactly by 8?
  40. 40.How many factors does 63 have?

Answer key

  1. 9
  2. 1
  3. 3
  4. 9
  5. 8
  6. 4
  7. 5944
  8. 6
  9. 4
  10. 2
  11. 4
  12. 4
  13. 3
  14. 5
  15. 7950
  16. 3
  17. 4
  18. 6519
  19. 2
  20. 2
  21. 1650
  22. 2
  23. 4
  24. 6
  25. 6
  26. 8
  27. 8
  28. 2805
  29. 5
  30. 1374
  31. 1
  32. 6
  33. 3172
  34. 1
  35. 5
  36. 2
  37. 1
  38. 6
  39. 3
  40. 6

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