Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 206 · 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) 8602 (b) 9101 (c) 7566 (d) 5984
2. 2.What is the smallest number you must add to 860 so that it divides exactly by 12?
3. 3.How many factors does 79 have?
4. 4.What is the smallest number you must take away from 954 so that it divides exactly by 13?
5. 5.What is the smallest number you must add to 263 so that it divides exactly by 12?
6. 6.How many factors does 65 have?
7. 7.Which of these numbers divides exactly by 6? (a) 8012 (b) 3438 (c) 2366 (d) 3485
8. 8.What is the smallest number you must add to 969 so that it divides exactly by 4?
9. 9.What is the smallest number you must take away from 757 so that it divides exactly by 12?
10. 10.Which of these numbers divides exactly by 6? (a) 1480 (b) 7466 (c) 9656 (d) 3432
11. 11.What is the smallest number you must add to 403 so that it divides exactly by 7?
12. 12.Which of these numbers divides exactly by 4? (a) 6785 (b) 5755 (c) 5222 (d) 5412
13. 13.How many factors does 71 have?
14. 14.What is the smallest number you must take away from 723 so that it divides exactly by 11?
15. 15.What is the smallest number you must add to 733 so that it divides exactly by 9?
16. 16.What is the smallest number you must take away from 647 so that it divides exactly by 11?
17. 17.How many factors does 60 have?
18. 18.What is the smallest number you must take away from 316 so that it divides exactly by 12?
19. 19.What is the smallest number you must take away from 260 so that it divides exactly by 6?
20. 20.Which of these numbers divides exactly by 4? (a) 5806 (b) 8448 (c) 6165 (d) 9797
21. 21.What is the smallest number you must take away from 871 so that it divides exactly by 6?
22. 22.How many factors does 20 have?
23. 23.What is the smallest number you must add to 973 so that it divides exactly by 9?
24. 24.What is the smallest number you must add to 993 so that it divides exactly by 4?
25. 25.Which of these numbers divides exactly by 8? (a) 7550 (b) 4525 (c) 5840 (d) 1271
26. 26.Which of these numbers divides exactly by 11? (a) 7326 (b) 9594 (c) 6202 (d) 7182
27. 27.How many factors does 97 have?
28. 28.What is the smallest number you must take away from 894 so that it divides exactly by 9?
29. 29.What is the smallest number you must take away from 505 so that it divides exactly by 4?
30. 30.What is the smallest number you must add to 406 so that it divides exactly by 13?
31. 31.What is the smallest number you must take away from 206 so that it divides exactly by 6?
32. 32.How many factors does 15 have?
33. 33.What is the smallest number you must add to 522 so that it divides exactly by 7?
34. 34.How many factors does 98 have?
35. 35.How many factors does 72 have?
36. 36.How many factors does 51 have?
37. 37.Which of these numbers divides exactly by 4? (a) 8765 (b) 2276 (c) 3129 (d) 1685
38. 38.How many factors does 92 have?
39. 39.What is the smallest number you must add to 765 so that it divides exactly by 8?
40. 40.What is the smallest number you must take away from 886 so that it divides exactly by 8?

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