Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 288 · 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 3? (a) 6425 (b) 2695 (c) 5580 (d) 6065
2. 2.What is the smallest number you must add to 777 so that it divides exactly by 4?
3. 3.How many factors does 84 have?
4. 4.What is the smallest number you must take away from 297 so that it divides exactly by 13?
5. 5.What is the smallest number you must add to 487 so that it divides exactly by 11?
6. 6.How many factors does 96 have?
7. 7.How many factors does 73 have?
8. 8.How many factors does 65 have?
9. 9.What is the smallest number you must take away from 101 so that it divides exactly by 13?
10. 10.What is the smallest number you must add to 164 so that it divides exactly by 13?
11. 11.What is the smallest number you must add to 472 so that it divides exactly by 7?
12. 12.How many factors does 31 have?
13. 13.What is the smallest number you must take away from 131 so that it divides exactly by 7?
14. 14.Which of these numbers divides exactly by 6? (a) 2882 (b) 6888 (c) 9827 (d) 5317
15. 15.How many factors does 20 have?
16. 16.What is the smallest number you must add to 296 so that it divides exactly by 11?
17. 17.What is the smallest number you must take away from 938 so that it divides exactly by 4?
18. 18.Which of these numbers divides exactly by 3? (a) 6631 (b) 5595 (c) 5677 (d) 8065
19. 19.What is the smallest number you must add to 634 so that it divides exactly by 3?
20. 20.Which of these numbers divides exactly by 11? (a) 8297 (b) 4675 (c) 1489 (d) 8033
21. 21.What is the smallest number you must add to 873 so that it divides exactly by 8?
22. 22.How many factors does 33 have?
23. 23.How many factors does 83 have?
24. 24.Which of these numbers divides exactly by 3? (a) 3109 (b) 6157 (c) 9708 (d) 3680
25. 25.What is the smallest number you must take away from 367 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 3? (a) 6803 (b) 8090 (c) 6753 (d) 4048
27. 27.How many factors does 60 have?
28. 28.What is the smallest number you must add to 700 so that it divides exactly by 9?
29. 29.Which of these numbers divides exactly by 9? (a) 4294 (b) 1212 (c) 7452 (d) 1552
30. 30.What is the smallest number you must take away from 548 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 6? (a) 4010 (b) 3204 (c) 1683 (d) 9700
32. 32.Which of these numbers divides exactly by 8? (a) 9026 (b) 2516 (c) 3680 (d) 6838
33. 33.What is the smallest number you must take away from 823 so that it divides exactly by 6?
34. 34.Which of these numbers divides exactly by 8? (a) 6234 (b) 5433 (c) 9296 (d) 9757
35. 35.What is the smallest number you must add to 679 so that it divides exactly by 3?
36. 36.How many factors does 27 have?
37. 37.How many factors does 21 have?
38. 38.What is the smallest number you must add to 159 so that it divides exactly by 4?
39. 39.How many factors does 14 have?
40. 40.What is the smallest number you must take away from 726 so that it divides exactly by 7?

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