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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 228 · 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 31 have?
  2. 2.How many factors does 65 have?
  3. 3.What is the smallest number you must add to 747 so that it divides exactly by 4?
  4. 4.Which of these numbers divides exactly by 6? (a) 3190 (b) 9405 (c) 2508 (d) 3413
  5. 5.How many factors does 72 have?
  6. 6.What is the smallest number you must take away from 802 so that it divides exactly by 3?
  7. 7.How many factors does 16 have?
  8. 8.How many factors does 92 have?
  9. 9.How many factors does 29 have?
  10. 10.What is the smallest number you must take away from 100 so that it divides exactly by 3?
  11. 11.What is the smallest number you must add to 387 so that it divides exactly by 8?
  12. 12.What is the smallest number you must add to 334 so that it divides exactly by 6?
  13. 13.How many factors does 25 have?
  14. 14.What is the smallest number you must add to 451 so that it divides exactly by 8?
  15. 15.What is the smallest number you must add to 674 so that it divides exactly by 6?
  16. 16.How many factors does 61 have?
  17. 17.What is the smallest number you must add to 970 so that it divides exactly by 6?
  18. 18.What is the smallest number you must take away from 359 so that it divides exactly by 7?
  19. 19.How many factors does 45 have?
  20. 20.Which of these numbers divides exactly by 8? (a) 6648 (b) 3555 (c) 2926 (d) 2766
  21. 21.How many factors does 88 have?
  22. 22.Which of these numbers divides exactly by 3? (a) 9836 (b) 1322 (c) 8270 (d) 9657
  23. 23.How many factors does 35 have?
  24. 24.How many factors does 15 have?
  25. 25.Which of these numbers divides exactly by 11? (a) 9514 (b) 4520 (c) 5333 (d) 2805
  26. 26.Which of these numbers divides exactly by 9? (a) 3004 (b) 1374 (c) 5670 (d) 6580
  27. 27.Which of these numbers divides exactly by 11? (a) 6632 (b) 2124 (c) 4631 (d) 2293
  28. 28.What is the smallest number you must add to 676 so that it divides exactly by 8?
  29. 29.How many factors does 32 have?
  30. 30.What is the smallest number you must add to 113 so that it divides exactly by 12?
  31. 31.Which of these numbers divides exactly by 11? (a) 3638 (b) 2442 (c) 1027 (d) 5942
  32. 32.Which of these numbers divides exactly by 4? (a) 8574 (b) 5217 (c) 4882 (d) 4096
  33. 33.What is the smallest number you must take away from 201 so that it divides exactly by 9?
  34. 34.What is the smallest number you must take away from 347 so that it divides exactly by 4?
  35. 35.Which of these numbers divides exactly by 11? (a) 3206 (b) 3845 (c) 7658 (d) 7942
  36. 36.How many factors does 55 have?
  37. 37.How many factors does 63 have?
  38. 38.What is the smallest number you must add to 100 so that it divides exactly by 6?
  39. 39.Which of these numbers divides exactly by 9? (a) 1939 (b) 1695 (c) 3204 (d) 3466
  40. 40.What is the smallest number you must add to 647 so that it divides exactly by 4?

Answer key

  1. 2
  2. 4
  3. 1
  4. 2508
  5. 12
  6. 1
  7. 5
  8. 6
  9. 2
  10. 1
  11. 5
  12. 2
  13. 3
  14. 5
  15. 4
  16. 2
  17. 2
  18. 2
  19. 6
  20. 6648
  21. 8
  22. 9657
  23. 4
  24. 4
  25. 2805
  26. 5670
  27. 4631
  28. 4
  29. 6
  30. 7
  31. 2442
  32. 4096
  33. 3
  34. 3
  35. 7942
  36. 4
  37. 6
  38. 2
  39. 3204
  40. 1

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