Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 112 · 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) 6758 (b) 6555 (c) 8200 (d) 6143
2. 2.How many factors does 84 have?
3. 3.Which of these numbers divides exactly by 6? (a) 2670 (b) 2330 (c) 4718 (d) 1681
4. 4.Which of these numbers divides exactly by 4? (a) 8135 (b) 2854 (c) 3246 (d) 5620
5. 5.What is the smallest number you must add to 837 so that it divides exactly by 6?
6. 6.What is the smallest number you must add to 921 so that it divides exactly by 6?
7. 7.How many factors does 51 have?
8. 8.What is the smallest number you must add to 320 so that it divides exactly by 9?
9. 9.What is the smallest number you must take away from 315 so that it divides exactly by 6?
10. 10.What is the smallest number you must add to 222 so that it divides exactly by 13?
11. 11.How many factors does 72 have?
12. 12.Which of these numbers divides exactly by 3? (a) 7293 (b) 8134 (c) 3430 (d) 1684
13. 13.What is the smallest number you must add to 658 so that it divides exactly by 9?
14. 14.How many factors does 55 have?
15. 15.Which of these numbers divides exactly by 11? (a) 7379 (b) 4092 (c) 8815 (d) 5914
16. 16.What is the smallest number you must add to 769 so that it divides exactly by 13?
17. 17.How many factors does 14 have?
18. 18.What is the smallest number you must add to 248 so that it divides exactly by 6?
19. 19.Which of these numbers divides exactly by 3? (a) 3065 (b) 4139 (c) 7632 (d) 5897
20. 20.Which of these numbers divides exactly by 4? (a) 3278 (b) 3011 (c) 2232 (d) 7489
21. 21.Which of these numbers divides exactly by 11? (a) 3159 (b) 7739 (c) 3311 (d) 2715
22. 22.How many factors does 32 have?
23. 23.What is the smallest number you must take away from 215 so that it divides exactly by 7?
24. 24.What is the smallest number you must take away from 655 so that it divides exactly by 9?
25. 25.What is the smallest number you must add to 268 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 706 so that it divides exactly by 4?
27. 27.How many factors does 100 have?
28. 28.Which of these numbers divides exactly by 8? (a) 1195 (b) 7962 (c) 1632 (d) 4958
29. 29.Which of these numbers divides exactly by 3? (a) 6509 (b) 5085 (c) 6200 (d) 4300
30. 30.How many factors does 92 have?
31. 31.Which of these numbers divides exactly by 8? (a) 3238 (b) 2286 (c) 9479 (d) 4176
32. 32.Which of these numbers divides exactly by 6? (a) 8736 (b) 6752 (c) 3067 (d) 9329
33. 33.Which of these numbers divides exactly by 8? (a) 6256 (b) 8569 (c) 3591 (d) 6822
34. 34.What is the smallest number you must add to 513 so that it divides exactly by 6?
35. 35.How many factors does 31 have?
36. 36.Which of these numbers divides exactly by 4? (a) 6383 (b) 3127 (c) 5185 (d) 8168
37. 37.Which of these numbers divides exactly by 9? (a) 6413 (b) 7112 (c) 3846 (d) 1332
38. 38.Which of these numbers divides exactly by 4? (a) 7351 (b) 9839 (c) 1091 (d) 7460
39. 39.What is the smallest number you must add to 477 so that it divides exactly by 4?
40. 40.What is the smallest number you must add to 425 so that it divides exactly by 8?

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