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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 184 · 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 215 so that it divides exactly by 4?
  2. 2.What is the smallest number you must add to 865 so that it divides exactly by 3?
  3. 3.What is the smallest number you must add to 843 so that it divides exactly by 8?
  4. 4.How many factors does 39 have?
  5. 5.What is the smallest number you must add to 375 so that it divides exactly by 4?
  6. 6.Which of these numbers divides exactly by 8? (a) 7831 (b) 6969 (c) 3724 (d) 1816
  7. 7.How many factors does 30 have?
  8. 8.How many factors does 71 have?
  9. 9.How many factors does 40 have?
  10. 10.How many factors does 21 have?
  11. 11.What is the smallest number you must take away from 100 so that it divides exactly by 6?
  12. 12.Which of these numbers divides exactly by 9? (a) 7458 (b) 9990 (c) 7564 (d) 8548
  13. 13.How many factors does 80 have?
  14. 14.What is the smallest number you must add to 715 so that it divides exactly by 6?
  15. 15.Which of these numbers divides exactly by 11? (a) 5026 (b) 1998 (c) 8514 (d) 6140
  16. 16.Which of these numbers divides exactly by 4? (a) 5159 (b) 2498 (c) 4938 (d) 2700
  17. 17.What is the smallest number you must add to 220 so that it divides exactly by 13?
  18. 18.What is the smallest number you must take away from 994 so that it divides exactly by 3?
  19. 19.What is the smallest number you must take away from 497 so that it divides exactly by 3?
  20. 20.How many factors does 41 have?
  21. 21.How many factors does 29 have?
  22. 22.What is the smallest number you must take away from 128 so that it divides exactly by 6?
  23. 23.Which of these numbers divides exactly by 4? (a) 2698 (b) 4219 (c) 3592 (d) 2799
  24. 24.Which of these numbers divides exactly by 9? (a) 7301 (b) 4491 (c) 9616 (d) 2260
  25. 25.How many factors does 67 have?
  26. 26.Which of these numbers divides exactly by 3? (a) 1552 (b) 3659 (c) 5413 (d) 9501
  27. 27.How many factors does 94 have?
  28. 28.How many factors does 96 have?
  29. 29.How many factors does 54 have?
  30. 30.What is the smallest number you must add to 191 so that it divides exactly by 6?
  31. 31.How many factors does 64 have?
  32. 32.What is the smallest number you must add to 953 so that it divides exactly by 9?
  33. 33.What is the smallest number you must add to 451 so that it divides exactly by 6?
  34. 34.What is the smallest number you must add to 227 so that it divides exactly by 7?
  35. 35.Which of these numbers divides exactly by 9? (a) 9837 (b) 2482 (c) 7601 (d) 6703
  36. 36.What is the smallest number you must add to 220 so that it divides exactly by 12?
  37. 37.Which of these numbers divides exactly by 9? (a) 5829 (b) 4940 (c) 5292 (d) 7770
  38. 38.How many factors does 88 have?
  39. 39.What is the smallest number you must add to 303 so that it divides exactly by 11?
  40. 40.What is the smallest number you must take away from 576 so that it divides exactly by 7?

Answer key

  1. 3
  2. 2
  3. 5
  4. 4
  5. 1
  6. 1816
  7. 8
  8. 2
  9. 8
  10. 4
  11. 4
  12. 9990
  13. 10
  14. 5
  15. 8514
  16. 2700
  17. 1
  18. 1
  19. 2
  20. 2
  21. 2
  22. 2
  23. 3592
  24. 4491
  25. 2
  26. 9501
  27. 4
  28. 12
  29. 8
  30. 1
  31. 7
  32. 1
  33. 5
  34. 4
  35. 9837
  36. 8
  37. 5292
  38. 8
  39. 5
  40. 2

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