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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 280 · 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 658 so that it divides exactly by 9?
  2. 2.What is the smallest number you must take away from 802 so that it divides exactly by 8?
  3. 3.What is the smallest number you must add to 990 so that it divides exactly by 7?
  4. 4.What is the smallest number you must take away from 205 so that it divides exactly by 11?
  5. 5.What is the smallest number you must add to 335 so that it divides exactly by 3?
  6. 6.How many factors does 29 have?
  7. 7.What is the smallest number you must take away from 897 so that it divides exactly by 8?
  8. 8.What is the smallest number you must add to 595 so that it divides exactly by 11?
  9. 9.What is the smallest number you must take away from 482 so that it divides exactly by 7?
  10. 10.What is the smallest number you must take away from 522 so that it divides exactly by 8?
  11. 11.What is the smallest number you must add to 208 so that it divides exactly by 7?
  12. 12.What is the smallest number you must add to 332 so that it divides exactly by 12?
  13. 13.What is the smallest number you must take away from 595 so that it divides exactly by 8?
  14. 14.What is the smallest number you must add to 952 so that it divides exactly by 13?
  15. 15.Which of these numbers divides exactly by 8? (a) 4204 (b) 5490 (c) 8776 (d) 2167
  16. 16.How many factors does 16 have?
  17. 17.Which of these numbers divides exactly by 8? (a) 3052 (b) 9450 (c) 6290 (d) 1376
  18. 18.What is the smallest number you must take away from 969 so that it divides exactly by 11?
  19. 19.What is the smallest number you must take away from 453 so that it divides exactly by 6?
  20. 20.What is the smallest number you must add to 222 so that it divides exactly by 4?
  21. 21.What is the smallest number you must take away from 155 so that it divides exactly by 13?
  22. 22.How many factors does 74 have?
  23. 23.What is the smallest number you must add to 625 so that it divides exactly by 6?
  24. 24.Which of these numbers divides exactly by 11? (a) 1442 (b) 8987 (c) 2106 (d) 8028
  25. 25.What is the smallest number you must take away from 615 so that it divides exactly by 7?
  26. 26.How many factors does 58 have?
  27. 27.What is the smallest number you must take away from 697 so that it divides exactly by 7?
  28. 28.What is the smallest number you must add to 421 so that it divides exactly by 12?
  29. 29.How many factors does 30 have?
  30. 30.What is the smallest number you must take away from 277 so that it divides exactly by 8?
  31. 31.How many factors does 97 have?
  32. 32.How many factors does 80 have?
  33. 33.Which of these numbers divides exactly by 3? (a) 7993 (b) 4210 (c) 2091 (d) 2977
  34. 34.How many factors does 53 have?
  35. 35.How many factors does 48 have?
  36. 36.What is the smallest number you must add to 122 so that it divides exactly by 6?
  37. 37.How many factors does 34 have?
  38. 38.What is the smallest number you must add to 905 so that it divides exactly by 7?
  39. 39.What is the smallest number you must add to 270 so that it divides exactly by 8?
  40. 40.Which of these numbers divides exactly by 9? (a) 1131 (b) 4592 (c) 3267 (d) 2081

Answer key

  1. 8
  2. 2
  3. 4
  4. 7
  5. 1
  6. 2
  7. 1
  8. 10
  9. 6
  10. 2
  11. 2
  12. 4
  13. 3
  14. 10
  15. 8776
  16. 5
  17. 1376
  18. 1
  19. 3
  20. 2
  21. 12
  22. 4
  23. 5
  24. 8987
  25. 6
  26. 4
  27. 4
  28. 11
  29. 8
  30. 5
  31. 2
  32. 10
  33. 2091
  34. 2
  35. 10
  36. 4
  37. 4
  38. 5
  39. 2
  40. 3267

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