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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 247 · 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 347 so that it divides exactly by 3?
  2. 2.What is the smallest number you must take away from 819 so that it divides exactly by 6?
  3. 3.What is the smallest number you must take away from 736 so that it divides exactly by 7?
  4. 4.What is the smallest number you must take away from 954 so that it divides exactly by 7?
  5. 5.How many factors does 85 have?
  6. 6.How many factors does 52 have?
  7. 7.What is the smallest number you must add to 598 so that it divides exactly by 6?
  8. 8.How many factors does 58 have?
  9. 9.Which of these numbers divides exactly by 3? (a) 3644 (b) 9258 (c) 9007 (d) 5519
  10. 10.How many factors does 64 have?
  11. 11.What is the smallest number you must add to 770 so that it divides exactly by 13?
  12. 12.How many factors does 41 have?
  13. 13.What is the smallest number you must add to 925 so that it divides exactly by 8?
  14. 14.Which of these numbers divides exactly by 4? (a) 1423 (b) 7629 (c) 8270 (d) 9660
  15. 15.How many factors does 46 have?
  16. 16.What is the smallest number you must take away from 622 so that it divides exactly by 11?
  17. 17.What is the smallest number you must add to 971 so that it divides exactly by 4?
  18. 18.What is the smallest number you must take away from 672 so that it divides exactly by 13?
  19. 19.What is the smallest number you must add to 485 so that it divides exactly by 8?
  20. 20.Which of these numbers divides exactly by 4? (a) 7484 (b) 6863 (c) 1643 (d) 1686
  21. 21.Which of these numbers divides exactly by 8? (a) 1396 (b) 3504 (c) 5889 (d) 6717
  22. 22.How many factors does 18 have?
  23. 23.What is the smallest number you must add to 143 so that it divides exactly by 6?
  24. 24.What is the smallest number you must take away from 854 so that it divides exactly by 8?
  25. 25.What is the smallest number you must add to 905 so that it divides exactly by 3?
  26. 26.What is the smallest number you must add to 292 so that it divides exactly by 7?
  27. 27.Which of these numbers divides exactly by 6? (a) 4728 (b) 2317 (c) 4081 (d) 6428
  28. 28.What is the smallest number you must take away from 437 so that it divides exactly by 11?
  29. 29.How many factors does 89 have?
  30. 30.How many factors does 72 have?
  31. 31.What is the smallest number you must add to 213 so that it divides exactly by 8?
  32. 32.How many factors does 19 have?
  33. 33.How many factors does 77 have?
  34. 34.How many factors does 80 have?
  35. 35.What is the smallest number you must take away from 224 so that it divides exactly by 13?
  36. 36.What is the smallest number you must add to 676 so that it divides exactly by 6?
  37. 37.What is the smallest number you must add to 236 so that it divides exactly by 12?
  38. 38.How many factors does 50 have?
  39. 39.Which of these numbers divides exactly by 6? (a) 5639 (b) 7945 (c) 8886 (d) 1739
  40. 40.What is the smallest number you must add to 146 so that it divides exactly by 12?

Answer key

  1. 2
  2. 3
  3. 1
  4. 2
  5. 4
  6. 6
  7. 2
  8. 4
  9. 9258
  10. 7
  11. 10
  12. 2
  13. 3
  14. 9660
  15. 4
  16. 6
  17. 1
  18. 9
  19. 3
  20. 7484
  21. 3504
  22. 6
  23. 1
  24. 6
  25. 1
  26. 2
  27. 4728
  28. 8
  29. 2
  30. 12
  31. 3
  32. 2
  33. 4
  34. 10
  35. 3
  36. 2
  37. 4
  38. 6
  39. 8886
  40. 10

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