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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 239 · 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.Which of these numbers divides exactly by 8? (a) 2013 (b) 2825 (c) 6011 (d) 1280
  2. 2.What is the smallest number you must take away from 347 so that it divides exactly by 3?
  3. 3.How many factors does 34 have?
  4. 4.What is the smallest number you must add to 217 so that it divides exactly by 8?
  5. 5.How many factors does 77 have?
  6. 6.What is the smallest number you must take away from 463 so that it divides exactly by 3?
  7. 7.How many factors does 24 have?
  8. 8.How many factors does 100 have?
  9. 9.How many factors does 63 have?
  10. 10.What is the smallest number you must take away from 325 so that it divides exactly by 6?
  11. 11.What is the smallest number you must add to 410 so that it divides exactly by 12?
  12. 12.What is the smallest number you must add to 113 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 263 so that it divides exactly by 3?
  14. 14.How many factors does 37 have?
  15. 15.What is the smallest number you must take away from 384 so that it divides exactly by 11?
  16. 16.How many factors does 76 have?
  17. 17.What is the smallest number you must add to 344 so that it divides exactly by 11?
  18. 18.Which of these numbers divides exactly by 3? (a) 2640 (b) 2831 (c) 1838 (d) 4451
  19. 19.What is the smallest number you must take away from 492 so that it divides exactly by 8?
  20. 20.What is the smallest number you must add to 363 so that it divides exactly by 7?
  21. 21.How many factors does 21 have?
  22. 22.What is the smallest number you must add to 148 so that it divides exactly by 9?
  23. 23.Which of these numbers divides exactly by 6? (a) 1851 (b) 2030 (c) 7860 (d) 2977
  24. 24.How many factors does 92 have?
  25. 25.What is the smallest number you must take away from 697 so that it divides exactly by 3?
  26. 26.What is the smallest number you must add to 438 so that it divides exactly by 13?
  27. 27.How many factors does 46 have?
  28. 28.Which of these numbers divides exactly by 4? (a) 7333 (b) 3187 (c) 3405 (d) 6500
  29. 29.Which of these numbers divides exactly by 3? (a) 1373 (b) 3276 (c) 9074 (d) 2387
  30. 30.What is the smallest number you must add to 154 so that it divides exactly by 12?
  31. 31.What is the smallest number you must add to 977 so that it divides exactly by 7?
  32. 32.What is the smallest number you must take away from 227 so that it divides exactly by 12?
  33. 33.What is the smallest number you must take away from 538 so that it divides exactly by 6?
  34. 34.What is the smallest number you must add to 407 so that it divides exactly by 13?
  35. 35.Which of these numbers divides exactly by 3? (a) 2995 (b) 7428 (c) 1624 (d) 9463
  36. 36.How many factors does 22 have?
  37. 37.Which of these numbers divides exactly by 11? (a) 5742 (b) 3577 (c) 1514 (d) 7088
  38. 38.How many factors does 56 have?
  39. 39.Which of these numbers divides exactly by 8? (a) 1033 (b) 8740 (c) 4050 (d) 7016
  40. 40.How many factors does 98 have?

Answer key

  1. 1280
  2. 2
  3. 4
  4. 7
  5. 4
  6. 1
  7. 8
  8. 9
  9. 6
  10. 1
  11. 10
  12. 4
  13. 2
  14. 2
  15. 10
  16. 6
  17. 8
  18. 2640
  19. 4
  20. 1
  21. 4
  22. 5
  23. 7860
  24. 6
  25. 1
  26. 4
  27. 4
  28. 6500
  29. 3276
  30. 2
  31. 3
  32. 11
  33. 4
  34. 9
  35. 7428
  36. 4
  37. 5742
  38. 8
  39. 7016
  40. 6

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