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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 270 · 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 450 so that it divides exactly by 11?
  2. 2.Which of these numbers divides exactly by 3? (a) 7762 (b) 8961 (c) 2047 (d) 1277
  3. 3.How many factors does 82 have?
  4. 4.How many factors does 53 have?
  5. 5.How many factors does 55 have?
  6. 6.What is the smallest number you must take away from 331 so that it divides exactly by 7?
  7. 7.How many factors does 90 have?
  8. 8.How many factors does 35 have?
  9. 9.How many factors does 75 have?
  10. 10.Which of these numbers divides exactly by 4? (a) 2649 (b) 8401 (c) 8364 (d) 9875
  11. 11.What is the smallest number you must take away from 869 so that it divides exactly by 3?
  12. 12.How many factors does 24 have?
  13. 13.What is the smallest number you must take away from 325 so that it divides exactly by 11?
  14. 14.How many factors does 36 have?
  15. 15.How many factors does 28 have?
  16. 16.What is the smallest number you must take away from 321 so that it divides exactly by 6?
  17. 17.What is the smallest number you must take away from 709 so that it divides exactly by 11?
  18. 18.What is the smallest number you must add to 105 so that it divides exactly by 8?
  19. 19.Which of these numbers divides exactly by 3? (a) 5054 (b) 6590 (c) 2757 (d) 9955
  20. 20.Which of these numbers divides exactly by 8? (a) 9052 (b) 3996 (c) 3623 (d) 8856
  21. 21.Which of these numbers divides exactly by 8? (a) 4143 (b) 1385 (c) 8372 (d) 2640
  22. 22.How many factors does 56 have?
  23. 23.What is the smallest number you must add to 971 so that it divides exactly by 4?
  24. 24.What is the smallest number you must add to 478 so that it divides exactly by 12?
  25. 25.How many factors does 45 have?
  26. 26.How many factors does 63 have?
  27. 27.How many factors does 98 have?
  28. 28.What is the smallest number you must take away from 274 so that it divides exactly by 7?
  29. 29.Which of these numbers divides exactly by 8? (a) 8537 (b) 6163 (c) 9664 (d) 8286
  30. 30.Which of these numbers divides exactly by 8? (a) 8923 (b) 9624 (c) 7428 (d) 6237
  31. 31.What is the smallest number you must add to 262 so that it divides exactly by 3?
  32. 32.How many factors does 50 have?
  33. 33.What is the smallest number you must take away from 639 so that it divides exactly by 8?
  34. 34.What is the smallest number you must take away from 133 so that it divides exactly by 3?
  35. 35.How many factors does 54 have?
  36. 36.Which of these numbers divides exactly by 3? (a) 9352 (b) 1669 (c) 7481 (d) 3771
  37. 37.Which of these numbers divides exactly by 3? (a) 6875 (b) 3586 (c) 8641 (d) 2856
  38. 38.What is the smallest number you must add to 312 so that it divides exactly by 9?
  39. 39.What is the smallest number you must add to 332 so that it divides exactly by 11?
  40. 40.What is the smallest number you must take away from 186 so that it divides exactly by 12?

Answer key

  1. 10
  2. 8961
  3. 4
  4. 2
  5. 4
  6. 2
  7. 12
  8. 4
  9. 6
  10. 8364
  11. 2
  12. 8
  13. 6
  14. 9
  15. 6
  16. 3
  17. 5
  18. 7
  19. 2757
  20. 8856
  21. 2640
  22. 8
  23. 1
  24. 2
  25. 6
  26. 6
  27. 6
  28. 1
  29. 9664
  30. 9624
  31. 2
  32. 6
  33. 7
  34. 1
  35. 8
  36. 3771
  37. 2856
  38. 3
  39. 9
  40. 6

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