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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 265 · 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 410 so that it divides exactly by 6?
  2. 2.What is the smallest number you must add to 310 so that it divides exactly by 3?
  3. 3.Which of these numbers divides exactly by 4? (a) 9421 (b) 8998 (c) 2816 (d) 1015
  4. 4.What is the smallest number you must take away from 303 so that it divides exactly by 9?
  5. 5.What is the smallest number you must take away from 350 so that it divides exactly by 9?
  6. 6.What is the smallest number you must add to 234 so that it divides exactly by 4?
  7. 7.Which of these numbers divides exactly by 6? (a) 7985 (b) 8667 (c) 5389 (d) 9216
  8. 8.How many factors does 44 have?
  9. 9.Which of these numbers divides exactly by 4? (a) 4029 (b) 1959 (c) 5266 (d) 8908
  10. 10.How many factors does 91 have?
  11. 11.What is the smallest number you must take away from 363 so that it divides exactly by 9?
  12. 12.What is the smallest number you must take away from 202 so that it divides exactly by 13?
  13. 13.What is the smallest number you must take away from 115 so that it divides exactly by 11?
  14. 14.How many factors does 50 have?
  15. 15.What is the smallest number you must take away from 851 so that it divides exactly by 9?
  16. 16.What is the smallest number you must take away from 242 so that it divides exactly by 3?
  17. 17.What is the smallest number you must add to 624 so that it divides exactly by 9?
  18. 18.Which of these numbers divides exactly by 3? (a) 2046 (b) 7777 (c) 5755 (d) 2276
  19. 19.What is the smallest number you must take away from 532 so that it divides exactly by 9?
  20. 20.How many factors does 64 have?
  21. 21.How many factors does 30 have?
  22. 22.Which of these numbers divides exactly by 3? (a) 7965 (b) 1330 (c) 3953 (d) 1756
  23. 23.What is the smallest number you must take away from 316 so that it divides exactly by 3?
  24. 24.What is the smallest number you must add to 732 so that it divides exactly by 8?
  25. 25.How many factors does 13 have?
  26. 26.What is the smallest number you must take away from 403 so that it divides exactly by 3?
  27. 27.What is the smallest number you must take away from 746 so that it divides exactly by 8?
  28. 28.What is the smallest number you must take away from 113 so that it divides exactly by 3?
  29. 29.What is the smallest number you must add to 726 so that it divides exactly by 8?
  30. 30.How many factors does 80 have?
  31. 31.What is the smallest number you must take away from 298 so that it divides exactly by 9?
  32. 32.What is the smallest number you must add to 360 so that it divides exactly by 7?
  33. 33.What is the smallest number you must take away from 644 so that it divides exactly by 9?
  34. 34.What is the smallest number you must add to 185 so that it divides exactly by 11?
  35. 35.What is the smallest number you must take away from 209 so that it divides exactly by 4?
  36. 36.What is the smallest number you must add to 213 so that it divides exactly by 12?
  37. 37.How many factors does 37 have?
  38. 38.How many factors does 41 have?
  39. 39.What is the smallest number you must add to 565 so that it divides exactly by 9?
  40. 40.Which of these numbers divides exactly by 11? (a) 9325 (b) 9452 (c) 4455 (d) 1790

Answer key

  1. 4
  2. 2
  3. 2816
  4. 6
  5. 8
  6. 2
  7. 9216
  8. 6
  9. 8908
  10. 4
  11. 3
  12. 7
  13. 5
  14. 6
  15. 5
  16. 2
  17. 6
  18. 2046
  19. 1
  20. 7
  21. 8
  22. 7965
  23. 1
  24. 4
  25. 2
  26. 1
  27. 2
  28. 2
  29. 2
  30. 10
  31. 1
  32. 4
  33. 5
  34. 2
  35. 1
  36. 3
  37. 2
  38. 2
  39. 2
  40. 4455

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