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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 236 · 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 578 so that it divides exactly by 3?
  2. 2.What is the smallest number you must add to 642 so that it divides exactly by 7?
  3. 3.How many factors does 41 have?
  4. 4.What is the smallest number you must add to 906 so that it divides exactly by 7?
  5. 5.How many factors does 87 have?
  6. 6.How many factors does 65 have?
  7. 7.What is the smallest number you must take away from 924 so that it divides exactly by 13?
  8. 8.What is the smallest number you must take away from 678 so that it divides exactly by 4?
  9. 9.How many factors does 85 have?
  10. 10.Which of these numbers divides exactly by 4? (a) 9387 (b) 8271 (c) 4874 (d) 3724
  11. 11.How many factors does 62 have?
  12. 12.Which of these numbers divides exactly by 4? (a) 2296 (b) 6577 (c) 2767 (d) 4954
  13. 13.How many factors does 26 have?
  14. 14.How many factors does 68 have?
  15. 15.What is the smallest number you must take away from 319 so that it divides exactly by 12?
  16. 16.How many factors does 29 have?
  17. 17.Which of these numbers divides exactly by 11? (a) 6653 (b) 3465 (c) 3068 (d) 8460
  18. 18.Which of these numbers divides exactly by 8? (a) 7658 (b) 1642 (c) 1408 (d) 4419
  19. 19.What is the smallest number you must take away from 116 so that it divides exactly by 11?
  20. 20.How many factors does 40 have?
  21. 21.What is the smallest number you must add to 275 so that it divides exactly by 9?
  22. 22.Which of these numbers divides exactly by 6? (a) 5321 (b) 4626 (c) 1251 (d) 8177
  23. 23.What is the smallest number you must take away from 145 so that it divides exactly by 9?
  24. 24.What is the smallest number you must add to 857 so that it divides exactly by 4?
  25. 25.How many factors does 100 have?
  26. 26.How many factors does 22 have?
  27. 27.What is the smallest number you must take away from 667 so that it divides exactly by 6?
  28. 28.What is the smallest number you must add to 691 so that it divides exactly by 3?
  29. 29.How many factors does 64 have?
  30. 30.What is the smallest number you must add to 347 so that it divides exactly by 11?
  31. 31.Which of these numbers divides exactly by 3? (a) 1759 (b) 2371 (c) 9865 (d) 5520
  32. 32.What is the smallest number you must take away from 925 so that it divides exactly by 12?
  33. 33.Which of these numbers divides exactly by 3? (a) 9029 (b) 2778 (c) 5528 (d) 5027
  34. 34.What is the smallest number you must take away from 739 so that it divides exactly by 4?
  35. 35.How many factors does 38 have?
  36. 36.How many factors does 51 have?
  37. 37.What is the smallest number you must add to 758 so that it divides exactly by 3?
  38. 38.What is the smallest number you must add to 261 so that it divides exactly by 8?
  39. 39.Which of these numbers divides exactly by 6? (a) 3553 (b) 1015 (c) 3554 (d) 2046
  40. 40.What is the smallest number you must add to 769 so that it divides exactly by 3?

Answer key

  1. 1
  2. 2
  3. 2
  4. 4
  5. 4
  6. 4
  7. 1
  8. 2
  9. 4
  10. 3724
  11. 4
  12. 2296
  13. 4
  14. 6
  15. 7
  16. 2
  17. 3465
  18. 1408
  19. 6
  20. 8
  21. 4
  22. 4626
  23. 1
  24. 3
  25. 9
  26. 4
  27. 1
  28. 2
  29. 7
  30. 5
  31. 5520
  32. 1
  33. 2778
  34. 3
  35. 4
  36. 4
  37. 1
  38. 3
  39. 2046
  40. 2

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