← Divisibility and factors lesson New set →

Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 125 · 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 453 so that it divides exactly by 12?
  2. 2.What is the smallest number you must add to 284 so that it divides exactly by 8?
  3. 3.What is the smallest number you must add to 488 so that it divides exactly by 11?
  4. 4.Which of these numbers divides exactly by 8? (a) 9296 (b) 1670 (c) 1274 (d) 3954
  5. 5.How many factors does 79 have?
  6. 6.What is the smallest number you must take away from 811 so that it divides exactly by 13?
  7. 7.How many factors does 99 have?
  8. 8.What is the smallest number you must add to 577 so that it divides exactly by 6?
  9. 9.How many factors does 24 have?
  10. 10.What is the smallest number you must add to 249 so that it divides exactly by 4?
  11. 11.Which of these numbers divides exactly by 9? (a) 2406 (b) 5499 (c) 5979 (d) 7201
  12. 12.What is the smallest number you must take away from 507 so that it divides exactly by 6?
  13. 13.Which of these numbers divides exactly by 6? (a) 9386 (b) 4948 (c) 1609 (d) 3528
  14. 14.Which of these numbers divides exactly by 8? (a) 7126 (b) 6838 (c) 4010 (d) 9152
  15. 15.What is the smallest number you must add to 125 so that it divides exactly by 12?
  16. 16.What is the smallest number you must add to 639 so that it divides exactly by 12?
  17. 17.What is the smallest number you must add to 659 so that it divides exactly by 3?
  18. 18.Which of these numbers divides exactly by 3? (a) 8924 (b) 6497 (c) 3510 (d) 1840
  19. 19.How many factors does 16 have?
  20. 20.Which of these numbers divides exactly by 4? (a) 1121 (b) 2658 (c) 3052 (d) 7370
  21. 21.How many factors does 35 have?
  22. 22.How many factors does 56 have?
  23. 23.What is the smallest number you must add to 472 so that it divides exactly by 6?
  24. 24.Which of these numbers divides exactly by 3? (a) 7677 (b) 1534 (c) 8771 (d) 3620
  25. 25.What is the smallest number you must take away from 900 so that it divides exactly by 8?
  26. 26.What is the smallest number you must take away from 235 so that it divides exactly by 11?
  27. 27.What is the smallest number you must take away from 786 so that it divides exactly by 8?
  28. 28.How many factors does 18 have?
  29. 29.What is the smallest number you must take away from 764 so that it divides exactly by 13?
  30. 30.How many factors does 33 have?
  31. 31.What is the smallest number you must take away from 344 so that it divides exactly by 11?
  32. 32.What is the smallest number you must take away from 707 so that it divides exactly by 9?
  33. 33.How many factors does 75 have?
  34. 34.How many factors does 90 have?
  35. 35.How many factors does 46 have?
  36. 36.What is the smallest number you must take away from 124 so that it divides exactly by 3?
  37. 37.How many factors does 54 have?
  38. 38.What is the smallest number you must add to 445 so that it divides exactly by 12?
  39. 39.What is the smallest number you must take away from 963 so that it divides exactly by 4?
  40. 40.How many factors does 86 have?

Answer key

  1. 3
  2. 4
  3. 7
  4. 9296
  5. 2
  6. 5
  7. 6
  8. 5
  9. 8
  10. 3
  11. 5499
  12. 3
  13. 3528
  14. 9152
  15. 7
  16. 9
  17. 1
  18. 3510
  19. 5
  20. 3052
  21. 4
  22. 8
  23. 2
  24. 7677
  25. 4
  26. 4
  27. 2
  28. 6
  29. 10
  30. 4
  31. 3
  32. 5
  33. 6
  34. 12
  35. 4
  36. 1
  37. 8
  38. 11
  39. 3
  40. 4

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