Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 1 · 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 9? (a) 2112 (b) 1646 (c) 8262 (d) 4164
2. 2.How many factors does 85 have?
3. 3.Which of these numbers divides exactly by 11? (a) 2230 (b) 8243 (c) 8045 (d) 7678
4. 4.Which of these numbers divides exactly by 9? (a) 2003 (b) 3293 (c) 5068 (d) 5814
5. 5.How many factors does 89 have?
6. 6.Which of these numbers divides exactly by 4? (a) 1385 (b) 3949 (c) 3290 (d) 1036
7. 7.What is the smallest number you must add to 491 so that it divides exactly by 7?
8. 8.Which of these numbers divides exactly by 6? (a) 6184 (b) 3159 (c) 3792 (d) 2481
9. 9.What is the smallest number you must add to 977 so that it divides exactly by 7?
10. 10.Which of these numbers divides exactly by 6? (a) 9562 (b) 7419 (c) 9972 (d) 3021
11. 11.What is the smallest number you must take away from 525 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 4? (a) 7794 (b) 1011 (c) 5144 (d) 3291
13. 13.How many factors does 71 have?
14. 14.How many factors does 88 have?
15. 15.What is the smallest number you must take away from 310 so that it divides exactly by 11?
16. 16.What is the smallest number you must add to 569 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 9? (a) 1358 (b) 6566 (c) 9261 (d) 7365
18. 18.What is the smallest number you must add to 838 so that it divides exactly by 12?
19. 19.What is the smallest number you must add to 849 so that it divides exactly by 7?
20. 20.What is the smallest number you must add to 766 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 4? (a) 3708 (b) 3235 (c) 7279 (d) 9395
22. 22.How many factors does 36 have?
23. 23.Which of these numbers divides exactly by 3? (a) 4525 (b) 3396 (c) 9539 (d) 2836
24. 24.What is the smallest number you must take away from 200 so that it divides exactly by 13?
25. 25.What is the smallest number you must add to 897 so that it divides exactly by 9?
26. 26.What is the smallest number you must take away from 361 so that it divides exactly by 6?
27. 27.How many factors does 13 have?
28. 28.How many factors does 52 have?
29. 29.What is the smallest number you must take away from 769 so that it divides exactly by 8?
30. 30.What is the smallest number you must take away from 140 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 9? (a) 6558 (b) 3654 (c) 1434 (d) 1145
32. 32.What is the smallest number you must take away from 615 so that it divides exactly by 11?
33. 33.Which of these numbers divides exactly by 9? (a) 8905 (b) 3195 (c) 5091 (d) 6773
34. 34.What is the smallest number you must add to 224 so that it divides exactly by 3?
35. 35.How many factors does 94 have?
36. 36.How many factors does 63 have?
37. 37.Which of these numbers divides exactly by 8? (a) 6349 (b) 4440 (c) 7137 (d) 8226
38. 38.What is the smallest number you must add to 701 so that it divides exactly by 4?
39. 39.What is the smallest number you must take away from 171 so that it divides exactly by 4?
40. 40.How many factors does 53 have?

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