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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 237 · 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 284 so that it divides exactly by 9?
  2. 2.How many factors does 97 have?
  3. 3.What is the smallest number you must take away from 987 so that it divides exactly by 9?
  4. 4.What is the smallest number you must take away from 223 so that it divides exactly by 13?
  5. 5.What is the smallest number you must take away from 595 so that it divides exactly by 9?
  6. 6.Which of these numbers divides exactly by 4? (a) 2288 (b) 6642 (c) 2586 (d) 4189
  7. 7.What is the smallest number you must add to 274 so that it divides exactly by 3?
  8. 8.How many factors does 45 have?
  9. 9.How many factors does 22 have?
  10. 10.How many factors does 63 have?
  11. 11.What is the smallest number you must add to 326 so that it divides exactly by 13?
  12. 12.What is the smallest number you must take away from 211 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 841 so that it divides exactly by 7?
  14. 14.How many factors does 85 have?
  15. 15.What is the smallest number you must add to 217 so that it divides exactly by 13?
  16. 16.Which of these numbers divides exactly by 8? (a) 7812 (b) 8025 (c) 7615 (d) 8424
  17. 17.How many factors does 35 have?
  18. 18.Which of these numbers divides exactly by 3? (a) 6806 (b) 1700 (c) 9926 (d) 3435
  19. 19.What is the smallest number you must take away from 332 so that it divides exactly by 9?
  20. 20.What is the smallest number you must add to 554 so that it divides exactly by 12?
  21. 21.How many factors does 65 have?
  22. 22.Which of these numbers divides exactly by 4? (a) 1870 (b) 9341 (c) 3609 (d) 5868
  23. 23.What is the smallest number you must add to 836 so that it divides exactly by 9?
  24. 24.What is the smallest number you must take away from 631 so that it divides exactly by 8?
  25. 25.What is the smallest number you must add to 357 so that it divides exactly by 11?
  26. 26.How many factors does 98 have?
  27. 27.What is the smallest number you must take away from 285 so that it divides exactly by 6?
  28. 28.What is the smallest number you must take away from 272 so that it divides exactly by 7?
  29. 29.What is the smallest number you must take away from 497 so that it divides exactly by 11?
  30. 30.How many factors does 17 have?
  31. 31.Which of these numbers divides exactly by 4? (a) 6036 (b) 7434 (c) 3191 (d) 8217
  32. 32.What is the smallest number you must take away from 428 so that it divides exactly by 6?
  33. 33.How many factors does 39 have?
  34. 34.What is the smallest number you must take away from 666 so that it divides exactly by 4?
  35. 35.What is the smallest number you must add to 919 so that it divides exactly by 7?
  36. 36.How many factors does 60 have?
  37. 37.Which of these numbers divides exactly by 4? (a) 9937 (b) 8264 (c) 7411 (d) 9507
  38. 38.Which of these numbers divides exactly by 3? (a) 1575 (b) 2273 (c) 5267 (d) 1006
  39. 39.What is the smallest number you must add to 562 so that it divides exactly by 3?
  40. 40.How many factors does 59 have?

Answer key

  1. 4
  2. 2
  3. 6
  4. 2
  5. 1
  6. 2288
  7. 2
  8. 6
  9. 4
  10. 6
  11. 12
  12. 3
  13. 1
  14. 4
  15. 4
  16. 8424
  17. 4
  18. 3435
  19. 8
  20. 10
  21. 4
  22. 5868
  23. 1
  24. 7
  25. 6
  26. 6
  27. 3
  28. 6
  29. 2
  30. 2
  31. 6036
  32. 2
  33. 4
  34. 2
  35. 5
  36. 12
  37. 8264
  38. 1575
  39. 2
  40. 2

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