Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 26 · 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.What is the smallest number you must take away from 654 so that it divides exactly by 8?
2. 2.What is the smallest number you must take away from 380 so that it divides exactly by 12?
3. 3.Which of these numbers divides exactly by 8? (a) 1232 (b) 7253 (c) 1244 (d) 8445
4. 4.What is the smallest number you must add to 350 so that it divides exactly by 3?
5. 5.What is the smallest number you must take away from 347 so that it divides exactly by 8?
6. 6.How many factors does 96 have?
7. 7.What is the smallest number you must add to 721 so that it divides exactly by 3?
8. 8.What is the smallest number you must add to 418 so that it divides exactly by 7?
9. 9.How many factors does 61 have?
10. 10.What is the smallest number you must take away from 477 so that it divides exactly by 12?
11. 11.Which of these numbers divides exactly by 3? (a) 1933 (b) 4602 (c) 7310 (d) 5498
12. 12.What is the smallest number you must add to 189 so that it divides exactly by 6?
13. 13.How many factors does 13 have?
14. 14.What is the smallest number you must add to 915 so that it divides exactly by 13?
15. 15.What is the smallest number you must add to 609 so that it divides exactly by 4?
16. 16.How many factors does 57 have?
17. 17.How many factors does 41 have?
18. 18.What is the smallest number you must add to 953 so that it divides exactly by 4?
19. 19.What is the smallest number you must add to 695 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 932 so that it divides exactly by 6?
21. 21.What is the smallest number you must take away from 427 so that it divides exactly by 6?
22. 22.Which of these numbers divides exactly by 8? (a) 1107 (b) 5912 (c) 9829 (d) 9337
23. 23.What is the smallest number you must take away from 935 so that it divides exactly by 6?
24. 24.What is the smallest number you must take away from 500 so that it divides exactly by 8?
25. 25.What is the smallest number you must add to 359 so that it divides exactly by 7?
26. 26.What is the smallest number you must take away from 706 so that it divides exactly by 12?
27. 27.What is the smallest number you must add to 224 so that it divides exactly by 9?
28. 28.Which of these numbers divides exactly by 8? (a) 9600 (b) 3175 (c) 9236 (d) 8692
29. 29.Which of these numbers divides exactly by 3? (a) 7547 (b) 3588 (c) 8771 (d) 3919
30. 30.How many factors does 34 have?
31. 31.How many factors does 52 have?
32. 32.What is the smallest number you must add to 886 so that it divides exactly by 9?
33. 33.How many factors does 83 have?
34. 34.How many factors does 91 have?
35. 35.How many factors does 49 have?
36. 36.How many factors does 85 have?
37. 37.What is the smallest number you must take away from 830 so that it divides exactly by 3?
38. 38.What is the smallest number you must add to 349 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 279 so that it divides exactly by 4?
40. 40.Which of these numbers divides exactly by 3? (a) 5820 (b) 8414 (c) 2879 (d) 2140

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