← Divisibility and factors lesson New set →

Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 182 · 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.Which of these numbers divides exactly by 3? (a) 5138 (b) 2715 (c) 8840 (d) 8450
  2. 2.What is the smallest number you must add to 411 so that it divides exactly by 8?
  3. 3.What is the smallest number you must add to 567 so that it divides exactly by 4?
  4. 4.Which of these numbers divides exactly by 3? (a) 5279 (b) 3295 (c) 1964 (d) 4014
  5. 5.How many factors does 65 have?
  6. 6.What is the smallest number you must take away from 953 so that it divides exactly by 9?
  7. 7.What is the smallest number you must take away from 745 so that it divides exactly by 3?
  8. 8.What is the smallest number you must add to 237 so that it divides exactly by 11?
  9. 9.How many factors does 32 have?
  10. 10.What is the smallest number you must take away from 331 so that it divides exactly by 8?
  11. 11.What is the smallest number you must add to 424 so that it divides exactly by 12?
  12. 12.What is the smallest number you must take away from 290 so that it divides exactly by 12?
  13. 13.What is the smallest number you must take away from 536 so that it divides exactly by 11?
  14. 14.How many factors does 45 have?
  15. 15.What is the smallest number you must add to 475 so that it divides exactly by 13?
  16. 16.Which of these numbers divides exactly by 9? (a) 9089 (b) 7842 (c) 3229 (d) 6786
  17. 17.How many factors does 83 have?
  18. 18.What is the smallest number you must add to 268 so that it divides exactly by 9?
  19. 19.What is the smallest number you must take away from 205 so that it divides exactly by 9?
  20. 20.Which of these numbers divides exactly by 3? (a) 3200 (b) 2048 (c) 7659 (d) 4216
  21. 21.What is the smallest number you must add to 717 so that it divides exactly by 6?
  22. 22.Which of these numbers divides exactly by 8? (a) 4640 (b) 1763 (c) 5217 (d) 1229
  23. 23.Which of these numbers divides exactly by 4? (a) 7826 (b) 4216 (c) 9649 (d) 5581
  24. 24.What is the smallest number you must take away from 641 so that it divides exactly by 6?
  25. 25.How many factors does 75 have?
  26. 26.Which of these numbers divides exactly by 9? (a) 3094 (b) 1682 (c) 8442 (d) 9355
  27. 27.What is the smallest number you must take away from 430 so that it divides exactly by 6?
  28. 28.How many factors does 58 have?
  29. 29.What is the smallest number you must take away from 414 so that it divides exactly by 12?
  30. 30.How many factors does 84 have?
  31. 31.How many factors does 19 have?
  32. 32.Which of these numbers divides exactly by 6? (a) 2664 (b) 6009 (c) 1845 (d) 5354
  33. 33.What is the smallest number you must take away from 731 so that it divides exactly by 13?
  34. 34.What is the smallest number you must add to 811 so that it divides exactly by 7?
  35. 35.What is the smallest number you must take away from 561 so that it divides exactly by 12?
  36. 36.What is the smallest number you must take away from 313 so that it divides exactly by 4?
  37. 37.How many factors does 24 have?
  38. 38.Which of these numbers divides exactly by 4? (a) 7542 (b) 8694 (c) 9019 (d) 8292
  39. 39.How many factors does 26 have?
  40. 40.What is the smallest number you must take away from 908 so that it divides exactly by 11?

Answer key

  1. 2715
  2. 5
  3. 1
  4. 4014
  5. 4
  6. 8
  7. 1
  8. 5
  9. 6
  10. 3
  11. 8
  12. 2
  13. 8
  14. 6
  15. 6
  16. 6786
  17. 2
  18. 2
  19. 7
  20. 7659
  21. 3
  22. 4640
  23. 4216
  24. 5
  25. 6
  26. 8442
  27. 4
  28. 4
  29. 6
  30. 12
  31. 2
  32. 2664
  33. 3
  34. 1
  35. 9
  36. 1
  37. 8
  38. 8292
  39. 4
  40. 6

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