Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 238 · 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.What is the smallest number you must add to 512 so that it divides exactly by 7?
2. 2.Which of these numbers divides exactly by 4? (a) 3577 (b) 6174 (c) 3424 (d) 9503
3. 3.How many factors does 74 have?
4. 4.How many factors does 57 have?
5. 5.How many factors does 28 have?
6. 6.What is the smallest number you must take away from 964 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 273 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 578 so that it divides exactly by 9?
9. 9.How many factors does 16 have?
10. 10.Which of these numbers divides exactly by 6? (a) 3208 (b) 2721 (c) 7218 (d) 7649
11. 11.How many factors does 71 have?
12. 12.What is the smallest number you must take away from 973 so that it divides exactly by 4?
13. 13.Which of these numbers divides exactly by 3? (a) 6200 (b) 8747 (c) 2604 (d) 7153
14. 14.Which of these numbers divides exactly by 3? (a) 4326 (b) 5813 (c) 2138 (d) 7321
15. 15.What is the smallest number you must add to 904 so that it divides exactly by 12?
16. 16.What is the smallest number you must take away from 997 so that it divides exactly by 7?
17. 17.What is the smallest number you must take away from 604 so that it divides exactly by 8?
18. 18.What is the smallest number you must add to 760 so that it divides exactly by 6?
19. 19.What is the smallest number you must add to 618 so that it divides exactly by 13?
20. 20.What is the smallest number you must add to 242 so that it divides exactly by 6?
21. 21.How many factors does 88 have?
22. 22.Which of these numbers divides exactly by 9? (a) 9643 (b) 4950 (c) 8954 (d) 9623
23. 23.Which of these numbers divides exactly by 11? (a) 2176 (b) 9542 (c) 1469 (d) 3905
24. 24.How many factors does 92 have?
25. 25.Which of these numbers divides exactly by 3? (a) 3517 (b) 5990 (c) 8798 (d) 8748
26. 26.What is the smallest number you must add to 643 so that it divides exactly by 3?
27. 27.What is the smallest number you must add to 195 so that it divides exactly by 9?
28. 28.How many factors does 34 have?
29. 29.What is the smallest number you must add to 255 so that it divides exactly by 7?
30. 30.How many factors does 96 have?
31. 31.How many factors does 23 have?
32. 32.Which of these numbers divides exactly by 6? (a) 9526 (b) 5825 (c) 2032 (d) 1998
33. 33.What is the smallest number you must add to 863 so that it divides exactly by 12?
34. 34.What is the smallest number you must take away from 627 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 8? (a) 2199 (b) 9672 (c) 6730 (d) 5053
36. 36.How many factors does 15 have?
37. 37.Which of these numbers divides exactly by 3? (a) 7708 (b) 2002 (c) 7990 (d) 8430
38. 38.Which of these numbers divides exactly by 3? (a) 6782 (b) 1459 (c) 1052 (d) 7158
39. 39.What is the smallest number you must add to 633 so that it divides exactly by 11?
40. 40.Which of these numbers divides exactly by 4? (a) 1677 (b) 9227 (c) 6293 (d) 5044

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