← Divisibility and factors lesson New set →

Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 195 · 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.How many factors does 19 have?
  2. 2.What is the smallest number you must add to 104 so that it divides exactly by 12?
  3. 3.How many factors does 96 have?
  4. 4.Which of these numbers divides exactly by 8? (a) 6644 (b) 6047 (c) 3248 (d) 9322
  5. 5.What is the smallest number you must take away from 498 so that it divides exactly by 9?
  6. 6.What is the smallest number you must add to 518 so that it divides exactly by 11?
  7. 7.What is the smallest number you must add to 595 so that it divides exactly by 6?
  8. 8.Which of these numbers divides exactly by 9? (a) 1840 (b) 3085 (c) 7298 (d) 7749
  9. 9.What is the smallest number you must add to 255 so that it divides exactly by 9?
  10. 10.What is the smallest number you must take away from 569 so that it divides exactly by 12?
  11. 11.Which of these numbers divides exactly by 3? (a) 9053 (b) 3343 (c) 2085 (d) 9689
  12. 12.How many factors does 31 have?
  13. 13.How many factors does 51 have?
  14. 14.What is the smallest number you must add to 307 so that it divides exactly by 6?
  15. 15.Which of these numbers divides exactly by 3? (a) 2920 (b) 6319 (c) 1086 (d) 2590
  16. 16.How many factors does 75 have?
  17. 17.What is the smallest number you must take away from 461 so that it divides exactly by 3?
  18. 18.How many factors does 38 have?
  19. 19.What is the smallest number you must take away from 124 so that it divides exactly by 11?
  20. 20.What is the smallest number you must take away from 295 so that it divides exactly by 4?
  21. 21.How many factors does 12 have?
  22. 22.How many factors does 76 have?
  23. 23.How many factors does 58 have?
  24. 24.Which of these numbers divides exactly by 6? (a) 2438 (b) 8590 (c) 7777 (d) 8118
  25. 25.How many factors does 78 have?
  26. 26.Which of these numbers divides exactly by 4? (a) 2570 (b) 5604 (c) 3141 (d) 9818
  27. 27.How many factors does 32 have?
  28. 28.How many factors does 24 have?
  29. 29.What is the smallest number you must add to 281 so that it divides exactly by 12?
  30. 30.Which of these numbers divides exactly by 4? (a) 7231 (b) 1469 (c) 2105 (d) 6368
  31. 31.Which of these numbers divides exactly by 11? (a) 3585 (b) 7189 (c) 1012 (d) 6879
  32. 32.What is the smallest number you must take away from 309 so that it divides exactly by 6?
  33. 33.How many factors does 28 have?
  34. 34.What is the smallest number you must add to 675 so that it divides exactly by 6?
  35. 35.What is the smallest number you must add to 825 so that it divides exactly by 12?
  36. 36.What is the smallest number you must take away from 612 so that it divides exactly by 13?
  37. 37.Which of these numbers divides exactly by 9? (a) 5842 (b) 1444 (c) 8096 (d) 4311
  38. 38.What is the smallest number you must take away from 619 so that it divides exactly by 3?
  39. 39.How many factors does 34 have?
  40. 40.What is the smallest number you must take away from 781 so that it divides exactly by 13?

Answer key

  1. 2
  2. 4
  3. 12
  4. 3248
  5. 3
  6. 10
  7. 5
  8. 7749
  9. 6
  10. 5
  11. 2085
  12. 2
  13. 4
  14. 5
  15. 1086
  16. 6
  17. 2
  18. 4
  19. 3
  20. 3
  21. 6
  22. 6
  23. 4
  24. 8118
  25. 8
  26. 5604
  27. 6
  28. 8
  29. 7
  30. 6368
  31. 1012
  32. 3
  33. 6
  34. 3
  35. 3
  36. 1
  37. 4311
  38. 1
  39. 4
  40. 1

Free quantitative aptitude lessons, practice and worksheets at talentjr.in/quantitative-aptitude