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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 271 · 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 580 so that it divides exactly by 11?
  2. 2.What is the smallest number you must add to 213 so that it divides exactly by 13?
  3. 3.What is the smallest number you must add to 537 so that it divides exactly by 4?
  4. 4.How many factors does 67 have?
  5. 5.How many factors does 58 have?
  6. 6.Which of these numbers divides exactly by 6? (a) 9107 (b) 2400 (c) 4257 (d) 1538
  7. 7.What is the smallest number you must add to 493 so that it divides exactly by 3?
  8. 8.Which of these numbers divides exactly by 6? (a) 2344 (b) 2310 (c) 2504 (d) 4831
  9. 9.What is the smallest number you must add to 121 so that it divides exactly by 13?
  10. 10.How many factors does 42 have?
  11. 11.How many factors does 94 have?
  12. 12.Which of these numbers divides exactly by 9? (a) 6939 (b) 2498 (c) 1929 (d) 2910
  13. 13.What is the smallest number you must add to 580 so that it divides exactly by 6?
  14. 14.How many factors does 79 have?
  15. 15.What is the smallest number you must add to 123 so that it divides exactly by 4?
  16. 16.What is the smallest number you must take away from 988 so that it divides exactly by 9?
  17. 17.What is the smallest number you must take away from 136 so that it divides exactly by 6?
  18. 18.How many factors does 70 have?
  19. 19.Which of these numbers divides exactly by 3? (a) 2647 (b) 4180 (c) 2724 (d) 3827
  20. 20.What is the smallest number you must add to 950 so that it divides exactly by 3?
  21. 21.What is the smallest number you must add to 316 so that it divides exactly by 11?
  22. 22.How many factors does 16 have?
  23. 23.Which of these numbers divides exactly by 8? (a) 1058 (b) 9520 (c) 9269 (d) 6519
  24. 24.What is the smallest number you must take away from 818 so that it divides exactly by 8?
  25. 25.Which of these numbers divides exactly by 4? (a) 1723 (b) 6459 (c) 1661 (d) 6408
  26. 26.What is the smallest number you must take away from 261 so that it divides exactly by 11?
  27. 27.How many factors does 68 have?
  28. 28.Which of these numbers divides exactly by 6? (a) 5510 (b) 8565 (c) 2082 (d) 1051
  29. 29.How many factors does 59 have?
  30. 30.How many factors does 45 have?
  31. 31.What is the smallest number you must take away from 885 so that it divides exactly by 6?
  32. 32.How many factors does 39 have?
  33. 33.Which of these numbers divides exactly by 9? (a) 4005 (b) 5928 (c) 6231 (d) 9412
  34. 34.How many factors does 30 have?
  35. 35.What is the smallest number you must add to 899 so that it divides exactly by 9?
  36. 36.Which of these numbers divides exactly by 11? (a) 4168 (b) 2860 (c) 2773 (d) 7985
  37. 37.What is the smallest number you must add to 250 so that it divides exactly by 7?
  38. 38.How many factors does 100 have?
  39. 39.Which of these numbers divides exactly by 4? (a) 5725 (b) 1200 (c) 3327 (d) 4717
  40. 40.What is the smallest number you must add to 350 so that it divides exactly by 3?

Answer key

  1. 8
  2. 8
  3. 3
  4. 2
  5. 4
  6. 2400
  7. 2
  8. 2310
  9. 9
  10. 8
  11. 4
  12. 6939
  13. 2
  14. 2
  15. 1
  16. 7
  17. 4
  18. 8
  19. 2724
  20. 1
  21. 3
  22. 5
  23. 9520
  24. 2
  25. 6408
  26. 8
  27. 6
  28. 2082
  29. 2
  30. 6
  31. 3
  32. 4
  33. 4005
  34. 8
  35. 1
  36. 2860
  37. 2
  38. 9
  39. 1200
  40. 1

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