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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 48 · 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 581 so that it divides exactly by 8?
  2. 2.Which of these numbers divides exactly by 6? (a) 5286 (b) 1629 (c) 1499 (d) 1624
  3. 3.How many factors does 22 have?
  4. 4.Which of these numbers divides exactly by 6? (a) 7827 (b) 2127 (c) 9095 (d) 8814
  5. 5.How many factors does 57 have?
  6. 6.How many factors does 64 have?
  7. 7.What is the smallest number you must take away from 821 so that it divides exactly by 6?
  8. 8.How many factors does 68 have?
  9. 9.What is the smallest number you must add to 620 so that it divides exactly by 13?
  10. 10.What is the smallest number you must take away from 897 so that it divides exactly by 9?
  11. 11.How many factors does 100 have?
  12. 12.Which of these numbers divides exactly by 3? (a) 3374 (b) 1634 (c) 8496 (d) 5026
  13. 13.How many factors does 51 have?
  14. 14.Which of these numbers divides exactly by 4? (a) 4895 (b) 9217 (c) 2007 (d) 5708
  15. 15.What is the smallest number you must take away from 394 so that it divides exactly by 8?
  16. 16.How many factors does 21 have?
  17. 17.How many factors does 69 have?
  18. 18.How many factors does 25 have?
  19. 19.What is the smallest number you must take away from 652 so that it divides exactly by 11?
  20. 20.How many factors does 32 have?
  21. 21.What is the smallest number you must add to 153 so that it divides exactly by 4?
  22. 22.How many factors does 75 have?
  23. 23.What is the smallest number you must take away from 267 so that it divides exactly by 7?
  24. 24.Which of these numbers divides exactly by 8? (a) 1676 (b) 4544 (c) 5349 (d) 1895
  25. 25.How many factors does 17 have?
  26. 26.Which of these numbers divides exactly by 11? (a) 7451 (b) 5128 (c) 4180 (d) 1962
  27. 27.What is the smallest number you must add to 918 so that it divides exactly by 13?
  28. 28.How many factors does 98 have?
  29. 29.What is the smallest number you must add to 829 so that it divides exactly by 8?
  30. 30.What is the smallest number you must take away from 876 so that it divides exactly by 9?
  31. 31.Which of these numbers divides exactly by 9? (a) 5580 (b) 8446 (c) 1021 (d) 5450
  32. 32.What is the smallest number you must add to 309 so that it divides exactly by 6?
  33. 33.What is the smallest number you must add to 395 so that it divides exactly by 11?
  34. 34.What is the smallest number you must take away from 329 so that it divides exactly by 12?
  35. 35.What is the smallest number you must take away from 339 so that it divides exactly by 6?
  36. 36.Which of these numbers divides exactly by 6? (a) 7177 (b) 8165 (c) 5328 (d) 7951
  37. 37.How many factors does 15 have?
  38. 38.Which of these numbers divides exactly by 3? (a) 3493 (b) 7084 (c) 7464 (d) 5390
  39. 39.What is the smallest number you must add to 956 so that it divides exactly by 7?
  40. 40.What is the smallest number you must add to 718 so that it divides exactly by 8?

Answer key

  1. 3
  2. 5286
  3. 4
  4. 8814
  5. 4
  6. 7
  7. 5
  8. 6
  9. 4
  10. 6
  11. 9
  12. 8496
  13. 4
  14. 5708
  15. 2
  16. 4
  17. 4
  18. 3
  19. 3
  20. 6
  21. 3
  22. 6
  23. 1
  24. 4544
  25. 2
  26. 4180
  27. 5
  28. 6
  29. 3
  30. 3
  31. 5580
  32. 3
  33. 1
  34. 5
  35. 3
  36. 5328
  37. 4
  38. 7464
  39. 3
  40. 2

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