Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 36 · 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 6? (a) 7280 (b) 9357 (c) 8962 (d) 3300
2. 2.How many factors does 66 have?
3. 3.What is the smallest number you must take away from 694 so that it divides exactly by 11?
4. 4.Which of these numbers divides exactly by 4? (a) 6687 (b) 9148 (c) 2330 (d) 7721
5. 5.How many factors does 43 have?
6. 6.Which of these numbers divides exactly by 3? (a) 6266 (b) 4540 (c) 7148 (d) 7710
7. 7.What is the smallest number you must take away from 259 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 646 so that it divides exactly by 4?
9. 9.How many factors does 32 have?
10. 10.How many factors does 14 have?
11. 11.Which of these numbers divides exactly by 3? (a) 7262 (b) 7739 (c) 2454 (d) 2465
12. 12.Which of these numbers divides exactly by 6? (a) 7232 (b) 4314 (c) 4817 (d) 7114
13. 13.How many factors does 83 have?
14. 14.What is the smallest number you must take away from 828 so that it divides exactly by 13?
15. 15.What is the smallest number you must add to 569 so that it divides exactly by 9?
16. 16.What is the smallest number you must add to 798 so that it divides exactly by 8?
17. 17.What is the smallest number you must take away from 320 so that it divides exactly by 9?
18. 18.How many factors does 27 have?
19. 19.What is the smallest number you must take away from 130 so that it divides exactly by 11?
20. 20.What is the smallest number you must take away from 519 so that it divides exactly by 9?
21. 21.Which of these numbers divides exactly by 6? (a) 8760 (b) 9682 (c) 3557 (d) 1153
22. 22.How many factors does 85 have?
23. 23.How many factors does 41 have?
24. 24.How many factors does 54 have?
25. 25.What is the smallest number you must add to 161 so that it divides exactly by 11?
26. 26.How many factors does 39 have?
27. 27.What is the smallest number you must take away from 397 so that it divides exactly by 3?
28. 28.What is the smallest number you must take away from 180 so that it divides exactly by 13?
29. 29.Which of these numbers divides exactly by 4? (a) 2931 (b) 1633 (c) 3645 (d) 2484
30. 30.How many factors does 67 have?
31. 31.What is the smallest number you must take away from 259 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 927 so that it divides exactly by 6?
33. 33.How many factors does 74 have?
34. 34.What is the smallest number you must take away from 722 so that it divides exactly by 8?
35. 35.Which of these numbers divides exactly by 6? (a) 7275 (b) 9916 (c) 9453 (d) 3558
36. 36.Which of these numbers divides exactly by 6? (a) 4551 (b) 9034 (c) 1246 (d) 9204
37. 37.Which of these numbers divides exactly by 11? (a) 1663 (b) 7887 (c) 7035 (d) 7377
38. 38.Which of these numbers divides exactly by 6? (a) 4855 (b) 1740 (c) 5120 (d) 6715
39. 39.What is the smallest number you must add to 535 so that it divides exactly by 4?
40. 40.What is the smallest number you must add to 983 so that it divides exactly by 3?

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