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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 15 · 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 610 so that it divides exactly by 4?
  2. 2.How many factors does 88 have?
  3. 3.How many factors does 69 have?
  4. 4.How many factors does 83 have?
  5. 5.How many factors does 20 have?
  6. 6.How many factors does 13 have?
  7. 7.How many factors does 80 have?
  8. 8.What is the smallest number you must take away from 121 so that it divides exactly by 3?
  9. 9.What is the smallest number you must take away from 557 so that it divides exactly by 4?
  10. 10.What is the smallest number you must add to 571 so that it divides exactly by 9?
  11. 11.What is the smallest number you must take away from 553 so that it divides exactly by 8?
  12. 12.How many factors does 18 have?
  13. 13.What is the smallest number you must take away from 379 so that it divides exactly by 8?
  14. 14.What is the smallest number you must take away from 238 so that it divides exactly by 8?
  15. 15.What is the smallest number you must add to 923 so that it divides exactly by 9?
  16. 16.What is the smallest number you must add to 669 so that it divides exactly by 13?
  17. 17.What is the smallest number you must take away from 972 so that it divides exactly by 13?
  18. 18.How many factors does 35 have?
  19. 19.How many factors does 56 have?
  20. 20.How many factors does 49 have?
  21. 21.What is the smallest number you must add to 834 so that it divides exactly by 7?
  22. 22.How many factors does 21 have?
  23. 23.What is the smallest number you must take away from 422 so that it divides exactly by 13?
  24. 24.Which of these numbers divides exactly by 4? (a) 5235 (b) 2406 (c) 5692 (d) 3466
  25. 25.What is the smallest number you must add to 590 so that it divides exactly by 3?
  26. 26.What is the smallest number you must take away from 331 so that it divides exactly by 6?
  27. 27.Which of these numbers divides exactly by 8? (a) 6906 (b) 4503 (c) 7495 (d) 8592
  28. 28.What is the smallest number you must add to 591 so that it divides exactly by 12?
  29. 29.Which of these numbers divides exactly by 8? (a) 2297 (b) 8758 (c) 8642 (d) 5624
  30. 30.How many factors does 58 have?
  31. 31.How many factors does 86 have?
  32. 32.What is the smallest number you must add to 620 so that it divides exactly by 9?
  33. 33.What is the smallest number you must add to 888 so that it divides exactly by 7?
  34. 34.How many factors does 33 have?
  35. 35.What is the smallest number you must add to 425 so that it divides exactly by 11?
  36. 36.Which of these numbers divides exactly by 4? (a) 2502 (b) 9396 (c) 8574 (d) 4325
  37. 37.How many factors does 37 have?
  38. 38.Which of these numbers divides exactly by 8? (a) 3842 (b) 3386 (c) 9088 (d) 2513
  39. 39.Which of these numbers divides exactly by 8? (a) 4835 (b) 9625 (c) 4392 (d) 8431
  40. 40.Which of these numbers divides exactly by 11? (a) 1979 (b) 7535 (c) 5869 (d) 3886

Answer key

  1. 2
  2. 8
  3. 4
  4. 2
  5. 6
  6. 2
  7. 10
  8. 1
  9. 1
  10. 5
  11. 1
  12. 6
  13. 3
  14. 6
  15. 4
  16. 7
  17. 10
  18. 4
  19. 8
  20. 3
  21. 6
  22. 4
  23. 6
  24. 5692
  25. 1
  26. 1
  27. 8592
  28. 9
  29. 5624
  30. 4
  31. 4
  32. 1
  33. 1
  34. 4
  35. 4
  36. 9396
  37. 2
  38. 9088
  39. 4392
  40. 7535

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