Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 114 · 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) 2714 (b) 4876 (c) 8779 (d) 2580
2. 2.Which of these numbers divides exactly by 3? (a) 3086 (b) 5181 (c) 8561 (d) 3224
3. 3.How many factors does 49 have?
4. 4.What is the smallest number you must add to 555 so that it divides exactly by 7?
5. 5.What is the smallest number you must add to 338 so that it divides exactly by 8?
6. 6.What is the smallest number you must take away from 626 so that it divides exactly by 7?
7. 7.Which of these numbers divides exactly by 6? (a) 3504 (b) 7394 (c) 7323 (d) 5014
8. 8.How many factors does 36 have?
9. 9.How many factors does 43 have?
10. 10.Which of these numbers divides exactly by 4? (a) 9148 (b) 7698 (c) 2667 (d) 5439
11. 11.Which of these numbers divides exactly by 4? (a) 1296 (b) 5019 (c) 5729 (d) 4442
12. 12.Which of these numbers divides exactly by 11? (a) 3542 (b) 8486 (c) 1427 (d) 2440
13. 13.What is the smallest number you must take away from 875 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 860 so that it divides exactly by 11?
15. 15.Which of these numbers divides exactly by 6? (a) 2543 (b) 3573 (c) 7476 (d) 2011
16. 16.What is the smallest number you must add to 314 so that it divides exactly by 11?
17. 17.How many factors does 99 have?
18. 18.What is the smallest number you must take away from 688 so that it divides exactly by 13?
19. 19.How many factors does 71 have?
20. 20.What is the smallest number you must add to 713 so that it divides exactly by 8?
21. 21.Which of these numbers divides exactly by 9? (a) 3009 (b) 1465 (c) 2151 (d) 6252
22. 22.What is the smallest number you must add to 990 so that it divides exactly by 8?
23. 23.What is the smallest number you must add to 406 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 8? (a) 5822 (b) 3049 (c) 1889 (d) 4752
25. 25.How many factors does 80 have?
26. 26.What is the smallest number you must take away from 604 so that it divides exactly by 9?
27. 27.Which of these numbers divides exactly by 3? (a) 1294 (b) 7736 (c) 1233 (d) 2603
28. 28.Which of these numbers divides exactly by 11? (a) 1838 (b) 7430 (c) 1267 (d) 6842
29. 29.How many factors does 81 have?
30. 30.What is the smallest number you must take away from 225 so that it divides exactly by 6?
31. 31.What is the smallest number you must take away from 296 so that it divides exactly by 11?
32. 32.How many factors does 32 have?
33. 33.Which of these numbers divides exactly by 8? (a) 6813 (b) 7888 (c) 6006 (d) 4009
34. 34.What is the smallest number you must take away from 303 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 11? (a) 7140 (b) 2283 (c) 2827 (d) 5689
36. 36.Which of these numbers divides exactly by 11? (a) 7512 (b) 2447 (c) 6754 (d) 4806
37. 37.Which of these numbers divides exactly by 11? (a) 8704 (b) 8771 (c) 1100 (d) 5391
38. 38.What is the smallest number you must take away from 990 so that it divides exactly by 13?
39. 39.What is the smallest number you must add to 729 so that it divides exactly by 7?
40. 40.Which of these numbers divides exactly by 4? (a) 5065 (b) 9581 (c) 9764 (d) 5485

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