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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 129 · 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.How many factors does 28 have?
  2. 2.What is the smallest number you must add to 534 so that it divides exactly by 9?
  3. 3.How many factors does 81 have?
  4. 4.What is the smallest number you must add to 960 so that it divides exactly by 7?
  5. 5.How many factors does 26 have?
  6. 6.What is the smallest number you must add to 676 so that it divides exactly by 8?
  7. 7.How many factors does 32 have?
  8. 8.Which of these numbers divides exactly by 9? (a) 8905 (b) 5006 (c) 6599 (d) 8874
  9. 9.What is the smallest number you must take away from 590 so that it divides exactly by 3?
  10. 10.What is the smallest number you must add to 353 so that it divides exactly by 13?
  11. 11.How many factors does 57 have?
  12. 12.What is the smallest number you must add to 969 so that it divides exactly by 7?
  13. 13.What is the smallest number you must add to 262 so that it divides exactly by 11?
  14. 14.Which of these numbers divides exactly by 9? (a) 1816 (b) 3664 (c) 2547 (d) 6502
  15. 15.What is the smallest number you must add to 301 so that it divides exactly by 3?
  16. 16.What is the smallest number you must take away from 773 so that it divides exactly by 13?
  17. 17.Which of these numbers divides exactly by 3? (a) 1445 (b) 5905 (c) 1743 (d) 4264
  18. 18.What is the smallest number you must add to 742 so that it divides exactly by 3?
  19. 19.Which of these numbers divides exactly by 3? (a) 4991 (b) 7541 (c) 6980 (d) 4404
  20. 20.What is the smallest number you must add to 912 so that it divides exactly by 11?
  21. 21.What is the smallest number you must take away from 964 so that it divides exactly by 11?
  22. 22.How many factors does 58 have?
  23. 23.Which of these numbers divides exactly by 4? (a) 9816 (b) 6625 (c) 2099 (d) 6558
  24. 24.How many factors does 36 have?
  25. 25.How many factors does 88 have?
  26. 26.How many factors does 20 have?
  27. 27.What is the smallest number you must take away from 778 so that it divides exactly by 7?
  28. 28.How many factors does 31 have?
  29. 29.What is the smallest number you must add to 824 so that it divides exactly by 13?
  30. 30.What is the smallest number you must take away from 273 so that it divides exactly by 6?
  31. 31.What is the smallest number you must take away from 311 so that it divides exactly by 9?
  32. 32.What is the smallest number you must take away from 740 so that it divides exactly by 8?
  33. 33.Which of these numbers divides exactly by 9? (a) 3963 (b) 3936 (c) 8478 (d) 1579
  34. 34.How many factors does 75 have?
  35. 35.How many factors does 43 have?
  36. 36.What is the smallest number you must take away from 734 so that it divides exactly by 13?
  37. 37.What is the smallest number you must take away from 216 so that it divides exactly by 11?
  38. 38.How many factors does 22 have?
  39. 39.Which of these numbers divides exactly by 3? (a) 2591 (b) 4336 (c) 2412 (d) 7592
  40. 40.What is the smallest number you must add to 109 so that it divides exactly by 8?

Answer key

  1. 6
  2. 6
  3. 5
  4. 6
  5. 4
  6. 4
  7. 6
  8. 8874
  9. 2
  10. 11
  11. 4
  12. 4
  13. 2
  14. 2547
  15. 2
  16. 6
  17. 1743
  18. 2
  19. 4404
  20. 1
  21. 7
  22. 4
  23. 9816
  24. 9
  25. 8
  26. 6
  27. 1
  28. 2
  29. 8
  30. 3
  31. 5
  32. 4
  33. 8478
  34. 6
  35. 2
  36. 6
  37. 7
  38. 4
  39. 2412
  40. 3

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