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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 188 · 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 48 have?
  2. 2.How many factors does 24 have?
  3. 3.How many factors does 86 have?
  4. 4.What is the smallest number you must take away from 945 so that it divides exactly by 4?
  5. 5.What is the smallest number you must take away from 751 so that it divides exactly by 12?
  6. 6.How many factors does 66 have?
  7. 7.Which of these numbers divides exactly by 4? (a) 4939 (b) 6174 (c) 2928 (d) 8559
  8. 8.What is the smallest number you must take away from 763 so that it divides exactly by 3?
  9. 9.What is the smallest number you must add to 241 so that it divides exactly by 6?
  10. 10.What is the smallest number you must add to 172 so that it divides exactly by 13?
  11. 11.What is the smallest number you must take away from 943 so that it divides exactly by 7?
  12. 12.How many factors does 50 have?
  13. 13.How many factors does 91 have?
  14. 14.Which of these numbers divides exactly by 6? (a) 1595 (b) 2053 (c) 9029 (d) 7890
  15. 15.How many factors does 68 have?
  16. 16.How many factors does 76 have?
  17. 17.How many factors does 34 have?
  18. 18.How many factors does 77 have?
  19. 19.How many factors does 71 have?
  20. 20.What is the smallest number you must add to 541 so that it divides exactly by 11?
  21. 21.Which of these numbers divides exactly by 9? (a) 2520 (b) 2194 (c) 6546 (d) 1889
  22. 22.How many factors does 45 have?
  23. 23.What is the smallest number you must take away from 958 so that it divides exactly by 7?
  24. 24.What is the smallest number you must take away from 167 so that it divides exactly by 13?
  25. 25.How many factors does 85 have?
  26. 26.What is the smallest number you must add to 173 so that it divides exactly by 3?
  27. 27.Which of these numbers divides exactly by 11? (a) 8228 (b) 8298 (c) 1031 (d) 5057
  28. 28.What is the smallest number you must take away from 609 so that it divides exactly by 11?
  29. 29.What is the smallest number you must take away from 817 so that it divides exactly by 12?
  30. 30.What is the smallest number you must take away from 138 so that it divides exactly by 11?
  31. 31.How many factors does 63 have?
  32. 32.What is the smallest number you must take away from 721 so that it divides exactly by 11?
  33. 33.Which of these numbers divides exactly by 6? (a) 4231 (b) 1537 (c) 8334 (d) 3737
  34. 34.What is the smallest number you must add to 907 so that it divides exactly by 6?
  35. 35.Which of these numbers divides exactly by 4? (a) 8913 (b) 9827 (c) 9421 (d) 5744
  36. 36.How many factors does 92 have?
  37. 37.What is the smallest number you must add to 956 so that it divides exactly by 11?
  38. 38.What is the smallest number you must add to 889 so that it divides exactly by 4?
  39. 39.What is the smallest number you must add to 137 so that it divides exactly by 3?
  40. 40.Which of these numbers divides exactly by 6? (a) 1327 (b) 9963 (c) 3988 (d) 9102

Answer key

  1. 10
  2. 8
  3. 4
  4. 1
  5. 7
  6. 8
  7. 2928
  8. 1
  9. 5
  10. 10
  11. 5
  12. 6
  13. 4
  14. 7890
  15. 6
  16. 6
  17. 4
  18. 4
  19. 2
  20. 9
  21. 2520
  22. 6
  23. 6
  24. 11
  25. 4
  26. 1
  27. 8228
  28. 4
  29. 1
  30. 6
  31. 6
  32. 6
  33. 8334
  34. 5
  35. 5744
  36. 6
  37. 1
  38. 3
  39. 1
  40. 9102

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