Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 197 · 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.How many factors does 21 have?
2. 2.What is the smallest number you must add to 975 so that it divides exactly by 7?
3. 3.Which of these numbers divides exactly by 4? (a) 7963 (b) 6755 (c) 1772 (d) 8831
4. 4.What is the smallest number you must take away from 442 so that it divides exactly by 11?
5. 5.Which of these numbers divides exactly by 6? (a) 8535 (b) 1572 (c) 6412 (d) 7517
6. 6.Which of these numbers divides exactly by 3? (a) 1963 (b) 6149 (c) 4444 (d) 6741
7. 7.Which of these numbers divides exactly by 3? (a) 3606 (b) 4675 (c) 1309 (d) 1423
8. 8.What is the smallest number you must add to 669 so that it divides exactly by 13?
9. 9.How many factors does 55 have?
10. 10.What is the smallest number you must take away from 260 so that it divides exactly by 3?
11. 11.Which of these numbers divides exactly by 8? (a) 9132 (b) 2116 (c) 7232 (d) 5882
12. 12.Which of these numbers divides exactly by 3? (a) 9748 (b) 1826 (c) 6362 (d) 9204
13. 13.How many factors does 29 have?
14. 14.How many factors does 27 have?
15. 15.How many factors does 39 have?
16. 16.What is the smallest number you must take away from 430 so that it divides exactly by 3?
17. 17.Which of these numbers divides exactly by 6? (a) 2014 (b) 4705 (c) 4458 (d) 4912
18. 18.What is the smallest number you must take away from 782 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 613 so that it divides exactly by 12?
20. 20.What is the smallest number you must add to 703 so that it divides exactly by 13?
21. 21.How many factors does 19 have?
22. 22.Which of these numbers divides exactly by 11? (a) 3544 (b) 3203 (c) 7297 (d) 5775
23. 23.What is the smallest number you must add to 327 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 629 so that it divides exactly by 3?
25. 25.How many factors does 82 have?
26. 26.What is the smallest number you must add to 691 so that it divides exactly by 3?
27. 27.How many factors does 65 have?
28. 28.How many factors does 33 have?
29. 29.Which of these numbers divides exactly by 9? (a) 1169 (b) 1265 (c) 6367 (d) 4248
30. 30.Which of these numbers divides exactly by 8? (a) 6283 (b) 7627 (c) 5259 (d) 1496
31. 31.How many factors does 94 have?
32. 32.What is the smallest number you must take away from 362 so that it divides exactly by 13?
33. 33.What is the smallest number you must take away from 230 so that it divides exactly by 4?
34. 34.Which of these numbers divides exactly by 9? (a) 9520 (b) 6876 (c) 9053 (d) 9395
35. 35.How many factors does 77 have?
36. 36.What is the smallest number you must add to 285 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 409 so that it divides exactly by 6?
38. 38.Which of these numbers divides exactly by 3? (a) 5951 (b) 5641 (c) 9141 (d) 3943
39. 39.What is the smallest number you must take away from 218 so that it divides exactly by 8?
40. 40.What is the smallest number you must take away from 602 so that it divides exactly by 8?

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