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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 63 · 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 946 so that it divides exactly by 8?
  2. 2.How many factors does 72 have?
  3. 3.How many factors does 37 have?
  4. 4.What is the smallest number you must take away from 915 so that it divides exactly by 7?
  5. 5.Which of these numbers divides exactly by 8? (a) 5978 (b) 7961 (c) 5032 (d) 9150
  6. 6.How many factors does 25 have?
  7. 7.What is the smallest number you must add to 707 so that it divides exactly by 6?
  8. 8.How many factors does 69 have?
  9. 9.How many factors does 38 have?
  10. 10.Which of these numbers divides exactly by 4? (a) 7655 (b) 8276 (c) 1437 (d) 4910
  11. 11.Which of these numbers divides exactly by 3? (a) 2504 (b) 4709 (c) 8728 (d) 1545
  12. 12.How many factors does 12 have?
  13. 13.What is the smallest number you must take away from 160 so that it divides exactly by 3?
  14. 14.Which of these numbers divides exactly by 4? (a) 7490 (b) 6235 (c) 3152 (d) 5141
  15. 15.What is the smallest number you must take away from 425 so that it divides exactly by 3?
  16. 16.How many factors does 29 have?
  17. 17.How many factors does 75 have?
  18. 18.How many factors does 63 have?
  19. 19.What is the smallest number you must add to 783 so that it divides exactly by 8?
  20. 20.What is the smallest number you must add to 225 so that it divides exactly by 11?
  21. 21.What is the smallest number you must take away from 208 so that it divides exactly by 7?
  22. 22.Which of these numbers divides exactly by 3? (a) 9627 (b) 1118 (c) 8254 (d) 4411
  23. 23.How many factors does 39 have?
  24. 24.How many factors does 36 have?
  25. 25.Which of these numbers divides exactly by 8? (a) 9003 (b) 5200 (c) 1729 (d) 2442
  26. 26.How many factors does 28 have?
  27. 27.What is the smallest number you must take away from 651 so that it divides exactly by 4?
  28. 28.What is the smallest number you must take away from 386 so that it divides exactly by 6?
  29. 29.How many factors does 16 have?
  30. 30.What is the smallest number you must add to 437 so that it divides exactly by 13?
  31. 31.How many factors does 66 have?
  32. 32.What is the smallest number you must add to 856 so that it divides exactly by 9?
  33. 33.Which of these numbers divides exactly by 4? (a) 1942 (b) 8421 (c) 7120 (d) 1855
  34. 34.What is the smallest number you must add to 274 so that it divides exactly by 12?
  35. 35.Which of these numbers divides exactly by 3? (a) 6160 (b) 3751 (c) 8416 (d) 2244
  36. 36.What is the smallest number you must take away from 608 so that it divides exactly by 9?
  37. 37.What is the smallest number you must take away from 779 so that it divides exactly by 11?
  38. 38.What is the smallest number you must take away from 394 so that it divides exactly by 11?
  39. 39.How many factors does 95 have?
  40. 40.What is the smallest number you must take away from 985 so that it divides exactly by 4?

Answer key

  1. 2
  2. 12
  3. 2
  4. 5
  5. 5032
  6. 3
  7. 1
  8. 4
  9. 4
  10. 8276
  11. 1545
  12. 6
  13. 1
  14. 3152
  15. 2
  16. 2
  17. 6
  18. 6
  19. 1
  20. 6
  21. 5
  22. 9627
  23. 4
  24. 9
  25. 5200
  26. 6
  27. 3
  28. 2
  29. 5
  30. 5
  31. 8
  32. 8
  33. 7120
  34. 2
  35. 2244
  36. 5
  37. 9
  38. 9
  39. 4
  40. 1

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