Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 135 · 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 19 have?
2. 2.How many factors does 16 have?
3. 3.What is the smallest number you must take away from 165 so that it divides exactly by 4?
4. 4.How many factors does 15 have?
5. 5.What is the smallest number you must add to 629 so that it divides exactly by 3?
6. 6.Which of these numbers divides exactly by 11? (a) 5066 (b) 2321 (c) 9884 (d) 8461
7. 7.Which of these numbers divides exactly by 4? (a) 1531 (b) 3051 (c) 7525 (d) 1300
8. 8.How many factors does 84 have?
9. 9.How many factors does 37 have?
10. 10.How many factors does 57 have?
11. 11.What is the smallest number you must add to 910 so that it divides exactly by 11?
12. 12.Which of these numbers divides exactly by 4? (a) 7164 (b) 3975 (c) 6121 (d) 7978
13. 13.Which of these numbers divides exactly by 11? (a) 3427 (b) 7249 (c) 2474 (d) 3752
14. 14.Which of these numbers divides exactly by 9? (a) 8664 (b) 8486 (c) 9392 (d) 4113
15. 15.What is the smallest number you must add to 403 so that it divides exactly by 8?
16. 16.How many factors does 75 have?
17. 17.Which of these numbers divides exactly by 6? (a) 1904 (b) 3498 (c) 9545 (d) 6749
18. 18.Which of these numbers divides exactly by 9? (a) 3015 (b) 7442 (c) 1520 (d) 3098
19. 19.What is the smallest number you must take away from 327 so that it divides exactly by 6?
20. 20.Which of these numbers divides exactly by 4? (a) 4304 (b) 1005 (c) 3353 (d) 8423
21. 21.Which of these numbers divides exactly by 8? (a) 7083 (b) 7257 (c) 6847 (d) 2880
22. 22.What is the smallest number you must take away from 747 so that it divides exactly by 6?
23. 23.How many factors does 24 have?
24. 24.What is the smallest number you must take away from 292 so that it divides exactly by 3?
25. 25.What is the smallest number you must add to 214 so that it divides exactly by 7?
26. 26.How many factors does 23 have?
27. 27.What is the smallest number you must take away from 773 so that it divides exactly by 8?
28. 28.Which of these numbers divides exactly by 9? (a) 5490 (b) 3910 (c) 8704 (d) 3481
29. 29.What is the smallest number you must take away from 599 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 314 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 8? (a) 7768 (b) 5878 (c) 9388 (d) 7817
32. 32.What is the smallest number you must add to 909 so that it divides exactly by 11?
33. 33.What is the smallest number you must add to 826 so that it divides exactly by 6?
34. 34.What is the smallest number you must add to 744 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 11? (a) 9652 (b) 9341 (c) 7287 (d) 4862
36. 36.What is the smallest number you must take away from 554 so that it divides exactly by 12?
37. 37.Which of these numbers divides exactly by 3? (a) 2996 (b) 5030 (c) 7556 (d) 2025
38. 38.What is the smallest number you must take away from 674 so that it divides exactly by 4?
39. 39.How many factors does 52 have?
40. 40.How many factors does 30 have?

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