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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 100 · 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 395 so that it divides exactly by 11?
  2. 2.What is the smallest number you must take away from 259 so that it divides exactly by 8?
  3. 3.What is the smallest number you must add to 688 so that it divides exactly by 11?
  4. 4.Which of these numbers divides exactly by 8? (a) 2175 (b) 1283 (c) 2064 (d) 6678
  5. 5.What is the smallest number you must take away from 260 so that it divides exactly by 3?
  6. 6.Which of these numbers divides exactly by 9? (a) 4468 (b) 7368 (c) 5878 (d) 6804
  7. 7.What is the smallest number you must add to 425 so that it divides exactly by 12?
  8. 8.What is the smallest number you must add to 219 so that it divides exactly by 9?
  9. 9.What is the smallest number you must take away from 118 so that it divides exactly by 13?
  10. 10.Which of these numbers divides exactly by 9? (a) 2674 (b) 4381 (c) 3837 (d) 5193
  11. 11.How many factors does 33 have?
  12. 12.How many factors does 99 have?
  13. 13.How many factors does 44 have?
  14. 14.What is the smallest number you must add to 501 so that it divides exactly by 4?
  15. 15.How many factors does 19 have?
  16. 16.Which of these numbers divides exactly by 3? (a) 2720 (b) 1214 (c) 4560 (d) 6727
  17. 17.Which of these numbers divides exactly by 3? (a) 3685 (b) 1992 (c) 4970 (d) 8759
  18. 18.Which of these numbers divides exactly by 6? (a) 1390 (b) 5526 (c) 1765 (d) 4315
  19. 19.What is the smallest number you must add to 912 so that it divides exactly by 13?
  20. 20.How many factors does 96 have?
  21. 21.What is the smallest number you must add to 803 so that it divides exactly by 12?
  22. 22.What is the smallest number you must add to 891 so that it divides exactly by 8?
  23. 23.What is the smallest number you must take away from 311 so that it divides exactly by 7?
  24. 24.Which of these numbers divides exactly by 4? (a) 3928 (b) 1871 (c) 3257 (d) 2551
  25. 25.What is the smallest number you must add to 950 so that it divides exactly by 4?
  26. 26.What is the smallest number you must take away from 763 so that it divides exactly by 3?
  27. 27.How many factors does 42 have?
  28. 28.How many factors does 16 have?
  29. 29.How many factors does 40 have?
  30. 30.How many factors does 46 have?
  31. 31.What is the smallest number you must take away from 246 so that it divides exactly by 4?
  32. 32.Which of these numbers divides exactly by 6? (a) 6012 (b) 3476 (c) 5541 (d) 5978
  33. 33.What is the smallest number you must take away from 546 so that it divides exactly by 9?
  34. 34.How many factors does 94 have?
  35. 35.How many factors does 86 have?
  36. 36.How many factors does 78 have?
  37. 37.How many factors does 85 have?
  38. 38.What is the smallest number you must add to 865 so that it divides exactly by 11?
  39. 39.What is the smallest number you must add to 749 so that it divides exactly by 11?
  40. 40.What is the smallest number you must add to 569 so that it divides exactly by 6?

Answer key

  1. 10
  2. 3
  3. 5
  4. 2064
  5. 2
  6. 6804
  7. 7
  8. 6
  9. 1
  10. 5193
  11. 4
  12. 6
  13. 6
  14. 3
  15. 2
  16. 4560
  17. 1992
  18. 5526
  19. 11
  20. 12
  21. 1
  22. 5
  23. 3
  24. 3928
  25. 2
  26. 1
  27. 8
  28. 5
  29. 8
  30. 4
  31. 2
  32. 6012
  33. 6
  34. 4
  35. 4
  36. 8
  37. 4
  38. 4
  39. 10
  40. 1

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