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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 190 · 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.Which of these numbers divides exactly by 6? (a) 4487 (b) 1185 (c) 2732 (d) 4350
  2. 2.What is the smallest number you must take away from 182 so that it divides exactly by 4?
  3. 3.What is the smallest number you must add to 644 so that it divides exactly by 11?
  4. 4.What is the smallest number you must add to 293 so that it divides exactly by 12?
  5. 5.What is the smallest number you must take away from 647 so that it divides exactly by 6?
  6. 6.How many factors does 65 have?
  7. 7.Which of these numbers divides exactly by 3? (a) 4377 (b) 3928 (c) 6073 (d) 2759
  8. 8.How many factors does 21 have?
  9. 9.What is the smallest number you must add to 234 so that it divides exactly by 7?
  10. 10.How many factors does 88 have?
  11. 11.What is the smallest number you must add to 709 so that it divides exactly by 12?
  12. 12.What is the smallest number you must take away from 266 so that it divides exactly by 4?
  13. 13.What is the smallest number you must take away from 567 so that it divides exactly by 8?
  14. 14.What is the smallest number you must add to 152 so that it divides exactly by 3?
  15. 15.What is the smallest number you must take away from 671 so that it divides exactly by 8?
  16. 16.What is the smallest number you must take away from 559 so that it divides exactly by 9?
  17. 17.What is the smallest number you must take away from 653 so that it divides exactly by 3?
  18. 18.How many factors does 58 have?
  19. 19.What is the smallest number you must add to 337 so that it divides exactly by 11?
  20. 20.Which of these numbers divides exactly by 3? (a) 3326 (b) 7263 (c) 1250 (d) 6581
  21. 21.What is the smallest number you must add to 321 so that it divides exactly by 13?
  22. 22.How many factors does 28 have?
  23. 23.Which of these numbers divides exactly by 4? (a) 6962 (b) 5916 (c) 1306 (d) 6841
  24. 24.Which of these numbers divides exactly by 4? (a) 5521 (b) 4039 (c) 7480 (d) 2395
  25. 25.What is the smallest number you must add to 240 so that it divides exactly by 9?
  26. 26.What is the smallest number you must take away from 562 so that it divides exactly by 9?
  27. 27.How many factors does 73 have?
  28. 28.What is the smallest number you must add to 955 so that it divides exactly by 4?
  29. 29.What is the smallest number you must add to 866 so that it divides exactly by 13?
  30. 30.What is the smallest number you must take away from 670 so that it divides exactly by 9?
  31. 31.What is the smallest number you must add to 413 so that it divides exactly by 6?
  32. 32.What is the smallest number you must take away from 874 so that it divides exactly by 12?
  33. 33.Which of these numbers divides exactly by 9? (a) 7915 (b) 2052 (c) 6960 (d) 9010
  34. 34.What is the smallest number you must add to 857 so that it divides exactly by 12?
  35. 35.How many factors does 48 have?
  36. 36.What is the smallest number you must take away from 654 so that it divides exactly by 8?
  37. 37.How many factors does 69 have?
  38. 38.What is the smallest number you must add to 327 so that it divides exactly by 4?
  39. 39.What is the smallest number you must add to 475 so that it divides exactly by 3?
  40. 40.What is the smallest number you must take away from 208 so that it divides exactly by 3?

Answer key

  1. 4350
  2. 2
  3. 5
  4. 7
  5. 5
  6. 4
  7. 4377
  8. 4
  9. 4
  10. 8
  11. 11
  12. 2
  13. 7
  14. 1
  15. 7
  16. 1
  17. 2
  18. 4
  19. 4
  20. 7263
  21. 4
  22. 6
  23. 5916
  24. 7480
  25. 3
  26. 4
  27. 2
  28. 1
  29. 5
  30. 4
  31. 1
  32. 10
  33. 2052
  34. 7
  35. 10
  36. 6
  37. 4
  38. 1
  39. 2
  40. 1

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