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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 310 · 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 take away from 201 so that it divides exactly by 9?
  2. 2.What is the smallest number you must add to 636 so that it divides exactly by 11?
  3. 3.What is the smallest number you must take away from 475 so that it divides exactly by 7?
  4. 4.How many factors does 12 have?
  5. 5.What is the smallest number you must take away from 780 so that it divides exactly by 11?
  6. 6.How many factors does 24 have?
  7. 7.What is the smallest number you must add to 407 so that it divides exactly by 13?
  8. 8.What is the smallest number you must add to 126 so that it divides exactly by 11?
  9. 9.Which of these numbers divides exactly by 4? (a) 7526 (b) 9393 (c) 1747 (d) 7736
  10. 10.How many factors does 35 have?
  11. 11.What is the smallest number you must add to 165 so that it divides exactly by 6?
  12. 12.How many factors does 28 have?
  13. 13.What is the smallest number you must add to 402 so that it divides exactly by 9?
  14. 14.How many factors does 49 have?
  15. 15.What is the smallest number you must add to 532 so that it divides exactly by 12?
  16. 16.What is the smallest number you must take away from 781 so that it divides exactly by 3?
  17. 17.What is the smallest number you must take away from 629 so that it divides exactly by 4?
  18. 18.What is the smallest number you must take away from 139 so that it divides exactly by 4?
  19. 19.What is the smallest number you must take away from 603 so that it divides exactly by 4?
  20. 20.How many factors does 48 have?
  21. 21.What is the smallest number you must add to 124 so that it divides exactly by 6?
  22. 22.What is the smallest number you must add to 835 so that it divides exactly by 7?
  23. 23.How many factors does 26 have?
  24. 24.How many factors does 32 have?
  25. 25.What is the smallest number you must add to 358 so that it divides exactly by 8?
  26. 26.Which of these numbers divides exactly by 9? (a) 2292 (b) 3493 (c) 4608 (d) 4235
  27. 27.What is the smallest number you must take away from 800 so that it divides exactly by 7?
  28. 28.What is the smallest number you must take away from 363 so that it divides exactly by 4?
  29. 29.How many factors does 91 have?
  30. 30.What is the smallest number you must add to 646 so that it divides exactly by 3?
  31. 31.Which of these numbers divides exactly by 11? (a) 2955 (b) 4667 (c) 6457 (d) 4953
  32. 32.What is the smallest number you must add to 171 so that it divides exactly by 13?
  33. 33.Which of these numbers divides exactly by 8? (a) 9607 (b) 3790 (c) 8104 (d) 2076
  34. 34.What is the smallest number you must take away from 805 so that it divides exactly by 13?
  35. 35.What is the smallest number you must add to 117 so that it divides exactly by 4?
  36. 36.How many factors does 69 have?
  37. 37.How many factors does 86 have?
  38. 38.What is the smallest number you must add to 515 so that it divides exactly by 11?
  39. 39.What is the smallest number you must take away from 947 so that it divides exactly by 11?
  40. 40.Which of these numbers divides exactly by 3? (a) 3434 (b) 5154 (c) 3589 (d) 8936

Answer key

  1. 3
  2. 2
  3. 6
  4. 6
  5. 10
  6. 8
  7. 9
  8. 6
  9. 7736
  10. 4
  11. 3
  12. 6
  13. 3
  14. 3
  15. 8
  16. 1
  17. 1
  18. 3
  19. 3
  20. 10
  21. 2
  22. 5
  23. 4
  24. 6
  25. 2
  26. 4608
  27. 2
  28. 3
  29. 4
  30. 2
  31. 6457
  32. 11
  33. 8104
  34. 12
  35. 3
  36. 4
  37. 4
  38. 2
  39. 1
  40. 5154

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