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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 312 · 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 11? (a) 1650 (b) 7277 (c) 6637 (d) 7844
  2. 2.Which of these numbers divides exactly by 11? (a) 4796 (b) 7340 (c) 3908 (d) 2642
  3. 3.Which of these numbers divides exactly by 6? (a) 7656 (b) 6501 (c) 9733 (d) 3209
  4. 4.What is the smallest number you must take away from 430 so that it divides exactly by 7?
  5. 5.What is the smallest number you must add to 236 so that it divides exactly by 12?
  6. 6.What is the smallest number you must take away from 821 so that it divides exactly by 13?
  7. 7.How many factors does 71 have?
  8. 8.What is the smallest number you must add to 458 so that it divides exactly by 12?
  9. 9.How many factors does 88 have?
  10. 10.What is the smallest number you must add to 640 so that it divides exactly by 13?
  11. 11.How many factors does 15 have?
  12. 12.How many factors does 96 have?
  13. 13.Which of these numbers divides exactly by 4? (a) 9265 (b) 7904 (c) 7533 (d) 1393
  14. 14.What is the smallest number you must take away from 861 so that it divides exactly by 6?
  15. 15.How many factors does 85 have?
  16. 16.How many factors does 17 have?
  17. 17.Which of these numbers divides exactly by 9? (a) 4740 (b) 6088 (c) 4167 (d) 6132
  18. 18.Which of these numbers divides exactly by 9? (a) 4583 (b) 9979 (c) 9316 (d) 9450
  19. 19.How many factors does 51 have?
  20. 20.Which of these numbers divides exactly by 6? (a) 5028 (b) 2255 (c) 7229 (d) 1981
  21. 21.Which of these numbers divides exactly by 4? (a) 2589 (b) 9893 (c) 6694 (d) 5544
  22. 22.What is the smallest number you must take away from 950 so that it divides exactly by 6?
  23. 23.What is the smallest number you must take away from 834 so that it divides exactly by 11?
  24. 24.What is the smallest number you must add to 749 so that it divides exactly by 3?
  25. 25.Which of these numbers divides exactly by 9? (a) 8420 (b) 2687 (c) 2007 (d) 2815
  26. 26.What is the smallest number you must take away from 159 so that it divides exactly by 4?
  27. 27.Which of these numbers divides exactly by 3? (a) 3844 (b) 5254 (c) 7386 (d) 2501
  28. 28.How many factors does 27 have?
  29. 29.Which of these numbers divides exactly by 8? (a) 7463 (b) 1704 (c) 1269 (d) 9766
  30. 30.How many factors does 64 have?
  31. 31.How many factors does 43 have?
  32. 32.What is the smallest number you must take away from 456 so that it divides exactly by 11?
  33. 33.How many factors does 49 have?
  34. 34.How many factors does 29 have?
  35. 35.How many factors does 33 have?
  36. 36.How many factors does 31 have?
  37. 37.What is the smallest number you must add to 374 so that it divides exactly by 6?
  38. 38.Which of these numbers divides exactly by 8? (a) 4965 (b) 6223 (c) 9776 (d) 1795
  39. 39.Which of these numbers divides exactly by 11? (a) 7518 (b) 1232 (c) 5529 (d) 3062
  40. 40.What is the smallest number you must take away from 953 so that it divides exactly by 6?

Answer key

  1. 1650
  2. 4796
  3. 7656
  4. 3
  5. 4
  6. 2
  7. 2
  8. 10
  9. 8
  10. 10
  11. 4
  12. 12
  13. 7904
  14. 3
  15. 4
  16. 2
  17. 4167
  18. 9450
  19. 4
  20. 5028
  21. 5544
  22. 2
  23. 9
  24. 1
  25. 2007
  26. 3
  27. 7386
  28. 4
  29. 1704
  30. 7
  31. 2
  32. 5
  33. 3
  34. 2
  35. 4
  36. 2
  37. 4
  38. 9776
  39. 1232
  40. 5

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