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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 25 · 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.How many factors does 44 have?
  2. 2.How many factors does 91 have?
  3. 3.What is the smallest number you must add to 532 so that it divides exactly by 3?
  4. 4.How many factors does 73 have?
  5. 5.Which of these numbers divides exactly by 4? (a) 7526 (b) 2709 (c) 7319 (d) 9112
  6. 6.Which of these numbers divides exactly by 6? (a) 4811 (b) 7239 (c) 2574 (d) 1829
  7. 7.How many factors does 65 have?
  8. 8.What is the smallest number you must add to 254 so that it divides exactly by 8?
  9. 9.What is the smallest number you must take away from 889 so that it divides exactly by 4?
  10. 10.How many factors does 54 have?
  11. 11.What is the smallest number you must add to 698 so that it divides exactly by 7?
  12. 12.Which of these numbers divides exactly by 9? (a) 9814 (b) 1443 (c) 5715 (d) 4709
  13. 13.What is the smallest number you must take away from 908 so that it divides exactly by 6?
  14. 14.How many factors does 52 have?
  15. 15.What is the smallest number you must take away from 803 so that it divides exactly by 8?
  16. 16.Which of these numbers divides exactly by 11? (a) 9295 (b) 5635 (c) 1101 (d) 8840
  17. 17.Which of these numbers divides exactly by 9? (a) 7219 (b) 7131 (c) 1202 (d) 2700
  18. 18.How many factors does 32 have?
  19. 19.What is the smallest number you must add to 403 so that it divides exactly by 9?
  20. 20.What is the smallest number you must add to 275 so that it divides exactly by 3?
  21. 21.Which of these numbers divides exactly by 6? (a) 9496 (b) 9629 (c) 3612 (d) 6743
  22. 22.Which of these numbers divides exactly by 11? (a) 4400 (b) 8652 (c) 9729 (d) 9017
  23. 23.How many factors does 36 have?
  24. 24.What is the smallest number you must add to 874 so that it divides exactly by 3?
  25. 25.What is the smallest number you must take away from 466 so that it divides exactly by 13?
  26. 26.How many factors does 23 have?
  27. 27.What is the smallest number you must take away from 304 so that it divides exactly by 7?
  28. 28.How many factors does 75 have?
  29. 29.What is the smallest number you must add to 253 so that it divides exactly by 6?
  30. 30.How many factors does 28 have?
  31. 31.Which of these numbers divides exactly by 3? (a) 1291 (b) 1546 (c) 2882 (d) 1743
  32. 32.How many factors does 68 have?
  33. 33.What is the smallest number you must add to 681 so that it divides exactly by 9?
  34. 34.What is the smallest number you must add to 644 so that it divides exactly by 11?
  35. 35.How many factors does 76 have?
  36. 36.Which of these numbers divides exactly by 9? (a) 3277 (b) 7489 (c) 4971 (d) 7272
  37. 37.What is the smallest number you must add to 942 so that it divides exactly by 12?
  38. 38.What is the smallest number you must add to 703 so that it divides exactly by 9?
  39. 39.What is the smallest number you must add to 970 so that it divides exactly by 8?
  40. 40.What is the smallest number you must take away from 997 so that it divides exactly by 12?

Answer key

  1. 6
  2. 4
  3. 2
  4. 2
  5. 9112
  6. 2574
  7. 4
  8. 2
  9. 1
  10. 8
  11. 2
  12. 5715
  13. 2
  14. 6
  15. 3
  16. 9295
  17. 2700
  18. 6
  19. 2
  20. 1
  21. 3612
  22. 4400
  23. 9
  24. 2
  25. 11
  26. 2
  27. 3
  28. 6
  29. 5
  30. 6
  31. 1743
  32. 6
  33. 3
  34. 5
  35. 6
  36. 7272
  37. 6
  38. 8
  39. 6
  40. 1

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