← Divisibility and factors lesson New set →

Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 148 · 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 47 have?
  2. 2.How many factors does 29 have?
  3. 3.Which of these numbers divides exactly by 11? (a) 2747 (b) 9109 (c) 8565 (d) 5148
  4. 4.How many factors does 84 have?
  5. 5.How many factors does 87 have?
  6. 6.How many factors does 44 have?
  7. 7.How many factors does 93 have?
  8. 8.What is the smallest number you must take away from 174 so that it divides exactly by 9?
  9. 9.Which of these numbers divides exactly by 11? (a) 6196 (b) 2288 (c) 1743 (d) 2487
  10. 10.Which of these numbers divides exactly by 9? (a) 7598 (b) 4328 (c) 2178 (d) 6213
  11. 11.What is the smallest number you must take away from 357 so that it divides exactly by 12?
  12. 12.What is the smallest number you must add to 117 so that it divides exactly by 8?
  13. 13.How many factors does 55 have?
  14. 14.Which of these numbers divides exactly by 11? (a) 3217 (b) 7462 (c) 7023 (d) 7106
  15. 15.What is the smallest number you must add to 303 so that it divides exactly by 4?
  16. 16.What is the smallest number you must add to 507 so that it divides exactly by 7?
  17. 17.What is the smallest number you must take away from 657 so that it divides exactly by 8?
  18. 18.Which of these numbers divides exactly by 11? (a) 8311 (b) 5389 (c) 1099 (d) 1298
  19. 19.How many factors does 17 have?
  20. 20.Which of these numbers divides exactly by 3? (a) 8839 (b) 1011 (c) 1445 (d) 3290
  21. 21.How many factors does 36 have?
  22. 22.What is the smallest number you must add to 730 so that it divides exactly by 11?
  23. 23.What is the smallest number you must take away from 790 so that it divides exactly by 8?
  24. 24.What is the smallest number you must add to 434 so that it divides exactly by 3?
  25. 25.What is the smallest number you must add to 678 so that it divides exactly by 12?
  26. 26.What is the smallest number you must take away from 136 so that it divides exactly by 3?
  27. 27.How many factors does 13 have?
  28. 28.What is the smallest number you must take away from 621 so that it divides exactly by 7?
  29. 29.What is the smallest number you must add to 446 so that it divides exactly by 7?
  30. 30.What is the smallest number you must add to 191 so that it divides exactly by 3?
  31. 31.What is the smallest number you must take away from 566 so that it divides exactly by 8?
  32. 32.What is the smallest number you must add to 247 so that it divides exactly by 8?
  33. 33.Which of these numbers divides exactly by 11? (a) 9977 (b) 8064 (c) 5920 (d) 5869
  34. 34.What is the smallest number you must add to 351 so that it divides exactly by 7?
  35. 35.How many factors does 96 have?
  36. 36.What is the smallest number you must take away from 958 so that it divides exactly by 8?
  37. 37.What is the smallest number you must take away from 543 so that it divides exactly by 12?
  38. 38.How many factors does 34 have?
  39. 39.What is the smallest number you must add to 455 so that it divides exactly by 6?
  40. 40.How many factors does 41 have?

Answer key

  1. 2
  2. 2
  3. 5148
  4. 12
  5. 4
  6. 6
  7. 4
  8. 3
  9. 2288
  10. 2178
  11. 9
  12. 3
  13. 4
  14. 7106
  15. 1
  16. 4
  17. 1
  18. 1298
  19. 2
  20. 1011
  21. 9
  22. 7
  23. 6
  24. 1
  25. 6
  26. 1
  27. 2
  28. 5
  29. 2
  30. 1
  31. 6
  32. 1
  33. 9977
  34. 6
  35. 12
  36. 6
  37. 3
  38. 4
  39. 1
  40. 2

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