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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 81 · 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 250 so that it divides exactly by 6?
  2. 2.What is the smallest number you must add to 635 so that it divides exactly by 12?
  3. 3.What is the smallest number you must add to 421 so that it divides exactly by 4?
  4. 4.What is the smallest number you must add to 385 so that it divides exactly by 4?
  5. 5.How many factors does 18 have?
  6. 6.What is the smallest number you must add to 698 so that it divides exactly by 4?
  7. 7.Which of these numbers divides exactly by 11? (a) 8264 (b) 7630 (c) 7697 (d) 4653
  8. 8.What is the smallest number you must add to 827 so that it divides exactly by 13?
  9. 9.How many factors does 31 have?
  10. 10.How many factors does 66 have?
  11. 11.How many factors does 83 have?
  12. 12.What is the smallest number you must add to 248 so that it divides exactly by 12?
  13. 13.What is the smallest number you must add to 491 so that it divides exactly by 7?
  14. 14.What is the smallest number you must add to 545 so that it divides exactly by 4?
  15. 15.How many factors does 42 have?
  16. 16.What is the smallest number you must add to 100 so that it divides exactly by 6?
  17. 17.What is the smallest number you must add to 211 so that it divides exactly by 3?
  18. 18.What is the smallest number you must add to 529 so that it divides exactly by 9?
  19. 19.What is the smallest number you must add to 282 so that it divides exactly by 11?
  20. 20.How many factors does 81 have?
  21. 21.What is the smallest number you must add to 879 so that it divides exactly by 6?
  22. 22.What is the smallest number you must add to 301 so that it divides exactly by 9?
  23. 23.How many factors does 53 have?
  24. 24.How many factors does 37 have?
  25. 25.What is the smallest number you must add to 134 so that it divides exactly by 6?
  26. 26.How many factors does 33 have?
  27. 27.How many factors does 69 have?
  28. 28.What is the smallest number you must take away from 753 so that it divides exactly by 12?
  29. 29.Which of these numbers divides exactly by 4? (a) 2821 (b) 2709 (c) 8394 (d) 9616
  30. 30.What is the smallest number you must take away from 619 so that it divides exactly by 3?
  31. 31.What is the smallest number you must take away from 189 so that it divides exactly by 6?
  32. 32.How many factors does 36 have?
  33. 33.Which of these numbers divides exactly by 6? (a) 3811 (b) 6196 (c) 6378 (d) 6376
  34. 34.Which of these numbers divides exactly by 6? (a) 2651 (b) 7132 (c) 6355 (d) 3456
  35. 35.What is the smallest number you must add to 116 so that it divides exactly by 12?
  36. 36.How many factors does 49 have?
  37. 37.How many factors does 51 have?
  38. 38.What is the smallest number you must take away from 302 so that it divides exactly by 11?
  39. 39.Which of these numbers divides exactly by 9? (a) 5544 (b) 6689 (c) 9404 (d) 4353
  40. 40.What is the smallest number you must add to 571 so that it divides exactly by 4?

Answer key

  1. 4
  2. 1
  3. 3
  4. 3
  5. 6
  6. 2
  7. 4653
  8. 5
  9. 2
  10. 8
  11. 2
  12. 4
  13. 6
  14. 3
  15. 8
  16. 2
  17. 2
  18. 2
  19. 4
  20. 5
  21. 3
  22. 5
  23. 2
  24. 2
  25. 4
  26. 4
  27. 4
  28. 9
  29. 9616
  30. 1
  31. 3
  32. 9
  33. 6378
  34. 3456
  35. 4
  36. 3
  37. 4
  38. 5
  39. 5544
  40. 1

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