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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 157 · 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 65 have?
  2. 2.What is the smallest number you must add to 358 so that it divides exactly by 12?
  3. 3.What is the smallest number you must add to 845 so that it divides exactly by 4?
  4. 4.What is the smallest number you must take away from 681 so that it divides exactly by 12?
  5. 5.How many factors does 32 have?
  6. 6.What is the smallest number you must take away from 116 so that it divides exactly by 8?
  7. 7.How many factors does 55 have?
  8. 8.How many factors does 79 have?
  9. 9.What is the smallest number you must add to 147 so that it divides exactly by 8?
  10. 10.What is the smallest number you must take away from 406 so that it divides exactly by 4?
  11. 11.How many factors does 41 have?
  12. 12.How many factors does 45 have?
  13. 13.Which of these numbers divides exactly by 3? (a) 7957 (b) 6461 (c) 4314 (d) 1897
  14. 14.Which of these numbers divides exactly by 4? (a) 7127 (b) 3763 (c) 8260 (d) 8625
  15. 15.How many factors does 82 have?
  16. 16.What is the smallest number you must add to 235 so that it divides exactly by 6?
  17. 17.How many factors does 61 have?
  18. 18.What is the smallest number you must take away from 473 so that it divides exactly by 6?
  19. 19.What is the smallest number you must add to 797 so that it divides exactly by 8?
  20. 20.What is the smallest number you must add to 308 so that it divides exactly by 6?
  21. 21.Which of these numbers divides exactly by 11? (a) 4081 (b) 2811 (c) 1139 (d) 6753
  22. 22.How many factors does 88 have?
  23. 23.Which of these numbers divides exactly by 9? (a) 1981 (b) 7400 (c) 4599 (d) 1871
  24. 24.What is the smallest number you must take away from 951 so that it divides exactly by 12?
  25. 25.What is the smallest number you must add to 995 so that it divides exactly by 9?
  26. 26.Which of these numbers divides exactly by 9? (a) 5880 (b) 6423 (c) 6606 (d) 8266
  27. 27.Which of these numbers divides exactly by 3? (a) 2459 (b) 5476 (c) 1920 (d) 6062
  28. 28.Which of these numbers divides exactly by 6? (a) 1096 (b) 9260 (c) 4638 (d) 3497
  29. 29.What is the smallest number you must add to 494 so that it divides exactly by 7?
  30. 30.What is the smallest number you must take away from 110 so that it divides exactly by 6?
  31. 31.How many factors does 42 have?
  32. 32.How many factors does 80 have?
  33. 33.How many factors does 53 have?
  34. 34.What is the smallest number you must take away from 274 so that it divides exactly by 3?
  35. 35.What is the smallest number you must take away from 151 so that it divides exactly by 12?
  36. 36.How many factors does 68 have?
  37. 37.How many factors does 44 have?
  38. 38.What is the smallest number you must take away from 991 so that it divides exactly by 9?
  39. 39.What is the smallest number you must take away from 686 so that it divides exactly by 9?
  40. 40.How many factors does 34 have?

Answer key

  1. 4
  2. 2
  3. 3
  4. 9
  5. 6
  6. 4
  7. 4
  8. 2
  9. 5
  10. 2
  11. 2
  12. 6
  13. 4314
  14. 8260
  15. 4
  16. 5
  17. 2
  18. 5
  19. 3
  20. 4
  21. 4081
  22. 8
  23. 4599
  24. 3
  25. 4
  26. 6606
  27. 1920
  28. 4638
  29. 3
  30. 2
  31. 8
  32. 10
  33. 2
  34. 1
  35. 7
  36. 6
  37. 6
  38. 1
  39. 2
  40. 4

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