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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 297 · 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 add to 227 so that it divides exactly by 9?
  2. 2.What is the smallest number you must add to 829 so that it divides exactly by 12?
  3. 3.What is the smallest number you must take away from 836 so that it divides exactly by 7?
  4. 4.What is the smallest number you must take away from 850 so that it divides exactly by 12?
  5. 5.How many factors does 79 have?
  6. 6.What is the smallest number you must add to 535 so that it divides exactly by 13?
  7. 7.What is the smallest number you must take away from 258 so that it divides exactly by 8?
  8. 8.How many factors does 24 have?
  9. 9.What is the smallest number you must take away from 645 so that it divides exactly by 11?
  10. 10.What is the smallest number you must add to 608 so that it divides exactly by 12?
  11. 11.Which of these numbers divides exactly by 3? (a) 2971 (b) 9090 (c) 5840 (d) 1598
  12. 12.How many factors does 20 have?
  13. 13.What is the smallest number you must add to 120 so that it divides exactly by 13?
  14. 14.How many factors does 100 have?
  15. 15.Which of these numbers divides exactly by 3? (a) 2827 (b) 9855 (c) 3394 (d) 6092
  16. 16.What is the smallest number you must add to 284 so that it divides exactly by 9?
  17. 17.What is the smallest number you must add to 428 so that it divides exactly by 3?
  18. 18.How many factors does 86 have?
  19. 19.What is the smallest number you must take away from 503 so that it divides exactly by 9?
  20. 20.What is the smallest number you must take away from 227 so that it divides exactly by 11?
  21. 21.What is the smallest number you must take away from 979 so that it divides exactly by 3?
  22. 22.What is the smallest number you must add to 826 so that it divides exactly by 8?
  23. 23.What is the smallest number you must take away from 235 so that it divides exactly by 3?
  24. 24.Which of these numbers divides exactly by 3? (a) 8383 (b) 2878 (c) 4991 (d) 5364
  25. 25.What is the smallest number you must take away from 874 so that it divides exactly by 7?
  26. 26.What is the smallest number you must add to 482 so that it divides exactly by 4?
  27. 27.How many factors does 27 have?
  28. 28.How many factors does 51 have?
  29. 29.How many factors does 15 have?
  30. 30.What is the smallest number you must add to 387 so that it divides exactly by 7?
  31. 31.What is the smallest number you must take away from 858 so that it divides exactly by 8?
  32. 32.How many factors does 21 have?
  33. 33.How many factors does 39 have?
  34. 34.What is the smallest number you must add to 298 so that it divides exactly by 4?
  35. 35.What is the smallest number you must take away from 803 so that it divides exactly by 13?
  36. 36.What is the smallest number you must take away from 212 so that it divides exactly by 7?
  37. 37.What is the smallest number you must add to 341 so that it divides exactly by 3?
  38. 38.How many factors does 66 have?
  39. 39.What is the smallest number you must take away from 626 so that it divides exactly by 8?
  40. 40.What is the smallest number you must take away from 811 so that it divides exactly by 12?

Answer key

  1. 7
  2. 11
  3. 3
  4. 10
  5. 2
  6. 11
  7. 2
  8. 8
  9. 7
  10. 4
  11. 9090
  12. 6
  13. 10
  14. 9
  15. 9855
  16. 4
  17. 1
  18. 4
  19. 8
  20. 7
  21. 1
  22. 6
  23. 1
  24. 5364
  25. 6
  26. 2
  27. 4
  28. 4
  29. 4
  30. 5
  31. 2
  32. 4
  33. 4
  34. 2
  35. 10
  36. 2
  37. 1
  38. 8
  39. 2
  40. 7

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