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Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 41 · 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 261 so that it divides exactly by 13?
  2. 2.What is the smallest number you must take away from 989 so that it divides exactly by 11?
  3. 3.What is the smallest number you must take away from 332 so that it divides exactly by 13?
  4. 4.How many factors does 64 have?
  5. 5.What is the smallest number you must add to 402 so that it divides exactly by 9?
  6. 6.Which of these numbers divides exactly by 11? (a) 4395 (b) 8597 (c) 1386 (d) 4176
  7. 7.What is the smallest number you must take away from 970 so that it divides exactly by 8?
  8. 8.What is the smallest number you must add to 193 so that it divides exactly by 7?
  9. 9.How many factors does 15 have?
  10. 10.What is the smallest number you must take away from 863 so that it divides exactly by 6?
  11. 11.What is the smallest number you must add to 194 so that it divides exactly by 11?
  12. 12.How many factors does 76 have?
  13. 13.How many factors does 99 have?
  14. 14.Which of these numbers divides exactly by 8? (a) 2749 (b) 4684 (c) 1888 (d) 1780
  15. 15.How many factors does 100 have?
  16. 16.How many factors does 74 have?
  17. 17.What is the smallest number you must take away from 604 so that it divides exactly by 13?
  18. 18.How many factors does 70 have?
  19. 19.Which of these numbers divides exactly by 9? (a) 2259 (b) 5488 (c) 4261 (d) 2096
  20. 20.What is the smallest number you must add to 179 so that it divides exactly by 12?
  21. 21.What is the smallest number you must add to 247 so that it divides exactly by 11?
  22. 22.What is the smallest number you must take away from 662 so that it divides exactly by 3?
  23. 23.What is the smallest number you must add to 485 so that it divides exactly by 9?
  24. 24.What is the smallest number you must add to 244 so that it divides exactly by 7?
  25. 25.How many factors does 37 have?
  26. 26.How many factors does 89 have?
  27. 27.How many factors does 83 have?
  28. 28.What is the smallest number you must take away from 263 so that it divides exactly by 7?
  29. 29.Which of these numbers divides exactly by 4? (a) 7312 (b) 8533 (c) 3902 (d) 4847
  30. 30.Which of these numbers divides exactly by 8? (a) 8422 (b) 6274 (c) 4712 (d) 7247
  31. 31.How many factors does 42 have?
  32. 32.Which of these numbers divides exactly by 3? (a) 2783 (b) 8194 (c) 5893 (d) 8838
  33. 33.What is the smallest number you must add to 370 so that it divides exactly by 13?
  34. 34.How many factors does 44 have?
  35. 35.What is the smallest number you must take away from 194 so that it divides exactly by 9?
  36. 36.How many factors does 52 have?
  37. 37.Which of these numbers divides exactly by 3? (a) 2603 (b) 4584 (c) 8330 (d) 2113
  38. 38.How many factors does 56 have?
  39. 39.How many factors does 43 have?
  40. 40.What is the smallest number you must take away from 241 so that it divides exactly by 9?

Answer key

  1. 1
  2. 10
  3. 7
  4. 7
  5. 3
  6. 1386
  7. 2
  8. 3
  9. 4
  10. 5
  11. 4
  12. 6
  13. 6
  14. 1888
  15. 9
  16. 4
  17. 6
  18. 8
  19. 2259
  20. 1
  21. 6
  22. 2
  23. 1
  24. 1
  25. 2
  26. 2
  27. 2
  28. 4
  29. 7312
  30. 4712
  31. 8
  32. 8838
  33. 7
  34. 6
  35. 5
  36. 6
  37. 4584
  38. 8
  39. 2
  40. 7

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