Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 74 · 40 questions

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.

1. 1.Which of these numbers divides exactly by 8? (a) 1079 (b) 8347 (c) 3897 (d) 8048
2. 2.What is the smallest number you must take away from 443 so that it divides exactly by 11?
3. 3.How many factors does 87 have?
4. 4.What is the smallest number you must add to 520 so that it divides exactly by 3?
5. 5.What is the smallest number you must take away from 665 so that it divides exactly by 13?
6. 6.What is the smallest number you must take away from 742 so that it divides exactly by 13?
7. 7.How many factors does 34 have?
8. 8.Which of these numbers divides exactly by 11? (a) 2389 (b) 1540 (c) 3166 (d) 8225
9. 9.What is the smallest number you must add to 272 so that it divides exactly by 11?
10. 10.What is the smallest number you must take away from 952 so that it divides exactly by 11?
11. 11.What is the smallest number you must add to 962 so that it divides exactly by 8?
12. 12.Which of these numbers divides exactly by 9? (a) 3681 (b) 5137 (c) 6801 (d) 9199
13. 13.Which of these numbers divides exactly by 6? (a) 4729 (b) 2562 (c) 1635 (d) 7568
14. 14.What is the smallest number you must add to 441 so that it divides exactly by 11?
15. 15.What is the smallest number you must take away from 550 so that it divides exactly by 6?
16. 16.What is the smallest number you must add to 598 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 3? (a) 4617 (b) 1519 (c) 9569 (d) 1343
18. 18.Which of these numbers divides exactly by 4? (a) 9430 (b) 7105 (c) 8669 (d) 3788
19. 19.How many factors does 48 have?
20. 20.How many factors does 14 have?
21. 21.How many factors does 41 have?
22. 22.What is the smallest number you must take away from 587 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 900 so that it divides exactly by 13?
24. 24.How many factors does 70 have?
25. 25.Which of these numbers divides exactly by 9? (a) 1158 (b) 7568 (c) 2163 (d) 2232
26. 26.What is the smallest number you must take away from 369 so that it divides exactly by 6?
27. 27.How many factors does 39 have?
28. 28.How many factors does 29 have?
29. 29.Which of these numbers divides exactly by 11? (a) 3696 (b) 7285 (c) 4815 (d) 6579
30. 30.How many factors does 17 have?
31. 31.Which of these numbers divides exactly by 3? (a) 5262 (b) 3277 (c) 2785 (d) 7591
32. 32.What is the smallest number you must add to 356 so that it divides exactly by 8?
33. 33.What is the smallest number you must take away from 734 so that it divides exactly by 4?
34. 34.How many factors does 47 have?
35. 35.Which of these numbers divides exactly by 3? (a) 8603 (b) 4187 (c) 2247 (d) 6799
36. 36.What is the smallest number you must take away from 796 so that it divides exactly by 9?
37. 37.How many factors does 31 have?
38. 38.What is the smallest number you must add to 880 so that it divides exactly by 3?
39. 39.Which of these numbers divides exactly by 11? (a) 1284 (b) 4983 (c) 5044 (d) 5955
40. 40.How many factors does 51 have?

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