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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 75 · 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 857 so that it divides exactly by 3?
  2. 2.What is the smallest number you must take away from 225 so that it divides exactly by 12?
  3. 3.What is the smallest number you must add to 601 so that it divides exactly by 11?
  4. 4.What is the smallest number you must take away from 460 so that it divides exactly by 13?
  5. 5.Which of these numbers divides exactly by 4? (a) 2802 (b) 3334 (c) 7391 (d) 6032
  6. 6.How many factors does 81 have?
  7. 7.What is the smallest number you must add to 108 so that it divides exactly by 11?
  8. 8.Which of these numbers divides exactly by 9? (a) 3404 (b) 7142 (c) 8476 (d) 4311
  9. 9.Which of these numbers divides exactly by 8? (a) 4357 (b) 3642 (c) 7905 (d) 7504
  10. 10.What is the smallest number you must take away from 990 so that it divides exactly by 12?
  11. 11.What is the smallest number you must take away from 279 so that it divides exactly by 8?
  12. 12.Which of these numbers divides exactly by 3? (a) 1576 (b) 4614 (c) 5849 (d) 7216
  13. 13.How many factors does 38 have?
  14. 14.How many factors does 29 have?
  15. 15.How many factors does 100 have?
  16. 16.How many factors does 33 have?
  17. 17.How many factors does 56 have?
  18. 18.How many factors does 46 have?
  19. 19.How many factors does 24 have?
  20. 20.What is the smallest number you must take away from 375 so that it divides exactly by 7?
  21. 21.How many factors does 73 have?
  22. 22.What is the smallest number you must take away from 324 so that it divides exactly by 8?
  23. 23.How many factors does 23 have?
  24. 24.Which of these numbers divides exactly by 8? (a) 7619 (b) 7373 (c) 5976 (d) 1683
  25. 25.How many factors does 96 have?
  26. 26.Which of these numbers divides exactly by 9? (a) 9212 (b) 1026 (c) 9229 (d) 8374
  27. 27.What is the smallest number you must add to 606 so that it divides exactly by 9?
  28. 28.Which of these numbers divides exactly by 3? (a) 5468 (b) 2820 (c) 4850 (d) 6023
  29. 29.How many factors does 92 have?
  30. 30.What is the smallest number you must add to 707 so that it divides exactly by 9?
  31. 31.How many factors does 16 have?
  32. 32.Which of these numbers divides exactly by 6? (a) 4742 (b) 3146 (c) 1542 (d) 5677
  33. 33.What is the smallest number you must add to 620 so that it divides exactly by 11?
  34. 34.Which of these numbers divides exactly by 3? (a) 9050 (b) 2280 (c) 6650 (d) 2828
  35. 35.Which of these numbers divides exactly by 9? (a) 6828 (b) 7452 (c) 5239 (d) 6190
  36. 36.What is the smallest number you must take away from 194 so that it divides exactly by 8?
  37. 37.How many factors does 47 have?
  38. 38.What is the smallest number you must take away from 628 so that it divides exactly by 6?
  39. 39.What is the smallest number you must take away from 904 so that it divides exactly by 6?
  40. 40.How many factors does 53 have?

Answer key

  1. 2
  2. 9
  3. 4
  4. 5
  5. 6032
  6. 5
  7. 2
  8. 4311
  9. 7504
  10. 6
  11. 7
  12. 4614
  13. 4
  14. 2
  15. 9
  16. 4
  17. 8
  18. 4
  19. 8
  20. 4
  21. 2
  22. 4
  23. 2
  24. 5976
  25. 12
  26. 1026
  27. 6
  28. 2820
  29. 6
  30. 4
  31. 5
  32. 1542
  33. 7
  34. 2280
  35. 7452
  36. 2
  37. 2
  38. 4
  39. 4
  40. 2

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