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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 187 · 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 add to 703 so that it divides exactly by 4?
  2. 2.What is the smallest number you must add to 444 so that it divides exactly by 8?
  3. 3.What is the smallest number you must add to 103 so that it divides exactly by 11?
  4. 4.How many factors does 32 have?
  5. 5.What is the smallest number you must take away from 533 so that it divides exactly by 4?
  6. 6.Which of these numbers divides exactly by 3? (a) 8545 (b) 1474 (c) 7890 (d) 8470
  7. 7.Which of these numbers divides exactly by 8? (a) 3610 (b) 1673 (c) 1497 (d) 5416
  8. 8.How many factors does 14 have?
  9. 9.What is the smallest number you must add to 129 so that it divides exactly by 8?
  10. 10.What is the smallest number you must take away from 567 so that it divides exactly by 8?
  11. 11.Which of these numbers divides exactly by 6? (a) 6692 (b) 1096 (c) 6912 (d) 8537
  12. 12.How many factors does 82 have?
  13. 13.What is the smallest number you must add to 162 so that it divides exactly by 12?
  14. 14.What is the smallest number you must add to 428 so that it divides exactly by 6?
  15. 15.How many factors does 22 have?
  16. 16.Which of these numbers divides exactly by 3? (a) 7511 (b) 1712 (c) 3247 (d) 1173
  17. 17.Which of these numbers divides exactly by 3? (a) 6266 (b) 4652 (c) 9521 (d) 1380
  18. 18.How many factors does 66 have?
  19. 19.What is the smallest number you must add to 628 so that it divides exactly by 13?
  20. 20.Which of these numbers divides exactly by 3? (a) 9734 (b) 2106 (c) 4889 (d) 1100
  21. 21.How many factors does 24 have?
  22. 22.How many factors does 25 have?
  23. 23.How many factors does 86 have?
  24. 24.What is the smallest number you must add to 184 so that it divides exactly by 11?
  25. 25.Which of these numbers divides exactly by 3? (a) 7312 (b) 9892 (c) 5635 (d) 8955
  26. 26.How many factors does 40 have?
  27. 27.What is the smallest number you must take away from 927 so that it divides exactly by 11?
  28. 28.Which of these numbers divides exactly by 6? (a) 4258 (b) 6897 (c) 2616 (d) 2551
  29. 29.How many factors does 17 have?
  30. 30.How many factors does 65 have?
  31. 31.What is the smallest number you must add to 387 so that it divides exactly by 8?
  32. 32.What is the smallest number you must take away from 131 so that it divides exactly by 9?
  33. 33.Which of these numbers divides exactly by 8? (a) 5464 (b) 6401 (c) 6867 (d) 2494
  34. 34.How many factors does 83 have?
  35. 35.Which of these numbers divides exactly by 11? (a) 1834 (b) 2475 (c) 5254 (d) 4168
  36. 36.Which of these numbers divides exactly by 9? (a) 1021 (b) 5438 (c) 8865 (d) 8880
  37. 37.Which of these numbers divides exactly by 6? (a) 7844 (b) 1674 (c) 2386 (d) 2303
  38. 38.Which of these numbers divides exactly by 11? (a) 1148 (b) 8883 (c) 3542 (d) 6309
  39. 39.How many factors does 42 have?
  40. 40.What is the smallest number you must add to 883 so that it divides exactly by 6?

Answer key

  1. 1
  2. 4
  3. 7
  4. 6
  5. 1
  6. 7890
  7. 5416
  8. 4
  9. 7
  10. 7
  11. 6912
  12. 4
  13. 6
  14. 4
  15. 4
  16. 1173
  17. 1380
  18. 8
  19. 9
  20. 2106
  21. 8
  22. 3
  23. 4
  24. 3
  25. 8955
  26. 8
  27. 3
  28. 2616
  29. 2
  30. 4
  31. 5
  32. 5
  33. 5464
  34. 2
  35. 2475
  36. 8865
  37. 1674
  38. 3542
  39. 8
  40. 5

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