Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 142 · 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) 7985 (b) 7650 (c) 7695 (d) 2884
2. 2.What is the smallest number you must add to 602 so that it divides exactly by 13?
3. 3.Which of these numbers divides exactly by 8? (a) 5798 (b) 2507 (c) 5926 (d) 3400
4. 4.What is the smallest number you must take away from 187 so that it divides exactly by 8?
5. 5.What is the smallest number you must take away from 871 so that it divides exactly by 3?
6. 6.How many factors does 43 have?
7. 7.How many factors does 53 have?
8. 8.What is the smallest number you must add to 597 so that it divides exactly by 12?
9. 9.How many factors does 59 have?
10. 10.What is the smallest number you must take away from 855 so that it divides exactly by 8?
11. 11.How many factors does 18 have?
12. 12.How many factors does 96 have?
13. 13.What is the smallest number you must add to 961 so that it divides exactly by 4?
14. 14.Which of these numbers divides exactly by 3? (a) 2821 (b) 2325 (c) 5834 (d) 9424
15. 15.What is the smallest number you must add to 991 so that it divides exactly by 8?
16. 16.What is the smallest number you must add to 694 so that it divides exactly by 8?
17. 17.How many factors does 57 have?
18. 18.What is the smallest number you must take away from 873 so that it divides exactly by 11?
19. 19.What is the smallest number you must take away from 989 so that it divides exactly by 3?
20. 20.What is the smallest number you must take away from 888 so that it divides exactly by 7?
21. 21.What is the smallest number you must take away from 790 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 625 so that it divides exactly by 7?
23. 23.How many factors does 21 have?
24. 24.What is the smallest number you must add to 867 so that it divides exactly by 11?
25. 25.How many factors does 13 have?
26. 26.What is the smallest number you must take away from 841 so that it divides exactly by 8?
27. 27.What is the smallest number you must add to 613 so that it divides exactly by 4?
28. 28.Which of these numbers divides exactly by 6? (a) 6385 (b) 8307 (c) 2106 (d) 5937
29. 29.How many factors does 23 have?
30. 30.How many factors does 34 have?
31. 31.What is the smallest number you must take away from 663 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 500 so that it divides exactly by 13?
33. 33.Which of these numbers divides exactly by 3? (a) 6125 (b) 6301 (c) 2446 (d) 6339
34. 34.What is the smallest number you must add to 827 so that it divides exactly by 3?
35. 35.What is the smallest number you must take away from 318 so that it divides exactly by 4?
36. 36.What is the smallest number you must add to 384 so that it divides exactly by 7?
37. 37.How many factors does 22 have?
38. 38.What is the smallest number you must take away from 591 so that it divides exactly by 4?
39. 39.How many factors does 35 have?
40. 40.Which of these numbers divides exactly by 9? (a) 8921 (b) 5665 (c) 1278 (d) 5018

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