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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 256 · 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 478 so that it divides exactly by 7?
  2. 2.What is the smallest number you must add to 279 so that it divides exactly by 6?
  3. 3.What is the smallest number you must add to 802 so that it divides exactly by 4?
  4. 4.What is the smallest number you must take away from 273 so that it divides exactly by 8?
  5. 5.What is the smallest number you must take away from 167 so that it divides exactly by 8?
  6. 6.Which of these numbers divides exactly by 3? (a) 7813 (b) 1688 (c) 9463 (d) 7239
  7. 7.What is the smallest number you must take away from 136 so that it divides exactly by 11?
  8. 8.What is the smallest number you must take away from 664 so that it divides exactly by 11?
  9. 9.How many factors does 44 have?
  10. 10.How many factors does 29 have?
  11. 11.How many factors does 48 have?
  12. 12.How many factors does 31 have?
  13. 13.Which of these numbers divides exactly by 6? (a) 2280 (b) 1109 (c) 3399 (d) 3235
  14. 14.How many factors does 78 have?
  15. 15.What is the smallest number you must add to 643 so that it divides exactly by 9?
  16. 16.How many factors does 19 have?
  17. 17.What is the smallest number you must take away from 290 so that it divides exactly by 6?
  18. 18.What is the smallest number you must add to 794 so that it divides exactly by 7?
  19. 19.How many factors does 96 have?
  20. 20.What is the smallest number you must add to 383 so that it divides exactly by 4?
  21. 21.What is the smallest number you must add to 631 so that it divides exactly by 11?
  22. 22.How many factors does 80 have?
  23. 23.Which of these numbers divides exactly by 8? (a) 2732 (b) 1673 (c) 2872 (d) 1365
  24. 24.How many factors does 24 have?
  25. 25.What is the smallest number you must take away from 103 so that it divides exactly by 6?
  26. 26.What is the smallest number you must add to 580 so that it divides exactly by 3?
  27. 27.How many factors does 28 have?
  28. 28.How many factors does 42 have?
  29. 29.Which of these numbers divides exactly by 9? (a) 8523 (b) 2870 (c) 5111 (d) 9178
  30. 30.What is the smallest number you must add to 174 so that it divides exactly by 7?
  31. 31.What is the smallest number you must add to 189 so that it divides exactly by 6?
  32. 32.Which of these numbers divides exactly by 11? (a) 5489 (b) 7536 (c) 7957 (d) 9377
  33. 33.What is the smallest number you must add to 577 so that it divides exactly by 11?
  34. 34.What is the smallest number you must add to 236 so that it divides exactly by 11?
  35. 35.How many factors does 58 have?
  36. 36.Which of these numbers divides exactly by 4? (a) 4427 (b) 7195 (c) 4636 (d) 5926
  37. 37.How many factors does 97 have?
  38. 38.How many factors does 79 have?
  39. 39.What is the smallest number you must take away from 593 so that it divides exactly by 7?
  40. 40.What is the smallest number you must add to 485 so that it divides exactly by 12?

Answer key

  1. 2
  2. 3
  3. 2
  4. 1
  5. 7
  6. 7239
  7. 4
  8. 4
  9. 6
  10. 2
  11. 10
  12. 2
  13. 2280
  14. 8
  15. 5
  16. 2
  17. 2
  18. 4
  19. 12
  20. 1
  21. 7
  22. 10
  23. 2872
  24. 8
  25. 1
  26. 2
  27. 6
  28. 8
  29. 8523
  30. 1
  31. 3
  32. 5489
  33. 6
  34. 6
  35. 4
  36. 4636
  37. 2
  38. 2
  39. 5
  40. 7

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