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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 6 · 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 18 have?
  2. 2.What is the smallest number you must add to 146 so that it divides exactly by 13?
  3. 3.What is the smallest number you must take away from 240 so that it divides exactly by 11?
  4. 4.How many factors does 78 have?
  5. 5.What is the smallest number you must take away from 709 so that it divides exactly by 7?
  6. 6.What is the smallest number you must add to 342 so that it divides exactly by 4?
  7. 7.What is the smallest number you must take away from 791 so that it divides exactly by 8?
  8. 8.Which of these numbers divides exactly by 8? (a) 9289 (b) 2065 (c) 4056 (d) 6823
  9. 9.Which of these numbers divides exactly by 8? (a) 2981 (b) 1512 (c) 4955 (d) 7164
  10. 10.What is the smallest number you must take away from 296 so that it divides exactly by 7?
  11. 11.What is the smallest number you must take away from 749 so that it divides exactly by 4?
  12. 12.How many factors does 58 have?
  13. 13.How many factors does 24 have?
  14. 14.What is the smallest number you must add to 110 so that it divides exactly by 8?
  15. 15.What is the smallest number you must add to 692 so that it divides exactly by 6?
  16. 16.What is the smallest number you must add to 372 so that it divides exactly by 9?
  17. 17.How many factors does 46 have?
  18. 18.Which of these numbers divides exactly by 6? (a) 1458 (b) 3344 (c) 6607 (d) 8157
  19. 19.Which of these numbers divides exactly by 8? (a) 5871 (b) 6536 (c) 3662 (d) 3139
  20. 20.Which of these numbers divides exactly by 4? (a) 6029 (b) 5514 (c) 8315 (d) 2156
  21. 21.Which of these numbers divides exactly by 11? (a) 5357 (b) 1009 (c) 2359 (d) 2682
  22. 22.Which of these numbers divides exactly by 3? (a) 1834 (b) 3542 (c) 2004 (d) 3034
  23. 23.What is the smallest number you must take away from 316 so that it divides exactly by 11?
  24. 24.How many factors does 67 have?
  25. 25.What is the smallest number you must take away from 277 so that it divides exactly by 6?
  26. 26.How many factors does 50 have?
  27. 27.How many factors does 39 have?
  28. 28.What is the smallest number you must add to 365 so that it divides exactly by 4?
  29. 29.How many factors does 34 have?
  30. 30.How many factors does 84 have?
  31. 31.What is the smallest number you must add to 374 so that it divides exactly by 6?
  32. 32.What is the smallest number you must add to 576 so that it divides exactly by 13?
  33. 33.How many factors does 19 have?
  34. 34.Which of these numbers divides exactly by 8? (a) 2270 (b) 6315 (c) 8408 (d) 9109
  35. 35.Which of these numbers divides exactly by 11? (a) 7643 (b) 6225 (c) 4237 (d) 8052
  36. 36.How many factors does 16 have?
  37. 37.How many factors does 79 have?
  38. 38.What is the smallest number you must take away from 725 so that it divides exactly by 4?
  39. 39.What is the smallest number you must add to 717 so that it divides exactly by 12?
  40. 40.How many factors does 35 have?

Answer key

  1. 6
  2. 10
  3. 9
  4. 8
  5. 2
  6. 2
  7. 7
  8. 4056
  9. 1512
  10. 2
  11. 1
  12. 4
  13. 8
  14. 2
  15. 4
  16. 6
  17. 4
  18. 1458
  19. 6536
  20. 2156
  21. 5357
  22. 2004
  23. 8
  24. 2
  25. 1
  26. 6
  27. 4
  28. 3
  29. 4
  30. 12
  31. 4
  32. 9
  33. 2
  34. 8408
  35. 8052
  36. 5
  37. 2
  38. 1
  39. 3
  40. 4

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