Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 205 · 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 add to 904 so that it divides exactly by 3?
2. 2.Which of these numbers divides exactly by 6? (a) 5092 (b) 9646 (c) 5444 (d) 3822
3. 3.Which of these numbers divides exactly by 6? (a) 5876 (b) 2391 (c) 7932 (d) 6325
4. 4.How many factors does 77 have?
5. 5.Which of these numbers divides exactly by 6? (a) 1127 (b) 8946 (c) 7493 (d) 3375
6. 6.How many factors does 76 have?
7. 7.Which of these numbers divides exactly by 4? (a) 2412 (b) 8610 (c) 5399 (d) 9825
8. 8.How many factors does 17 have?
9. 9.Which of these numbers divides exactly by 6? (a) 3730 (b) 4780 (c) 6179 (d) 2910
10. 10.What is the smallest number you must take away from 738 so that it divides exactly by 12?
11. 11.Which of these numbers divides exactly by 6? (a) 3252 (b) 6613 (c) 1933 (d) 5290
12. 12.How many factors does 51 have?
13. 13.What is the smallest number you must take away from 338 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 635 so that it divides exactly by 6?
15. 15.Which of these numbers divides exactly by 4? (a) 6903 (b) 3079 (c) 5172 (d) 2623
16. 16.What is the smallest number you must take away from 309 so that it divides exactly by 8?
17. 17.What is the smallest number you must add to 557 so that it divides exactly by 11?
18. 18.How many factors does 56 have?
19. 19.Which of these numbers divides exactly by 11? (a) 2406 (b) 4893 (c) 1858 (d) 8976
20. 20.What is the smallest number you must add to 273 so that it divides exactly by 12?
21. 21.What is the smallest number you must take away from 787 so that it divides exactly by 9?
22. 22.Which of these numbers divides exactly by 11? (a) 8989 (b) 2147 (c) 9377 (d) 4906
23. 23.Which of these numbers divides exactly by 3? (a) 7379 (b) 6866 (c) 4382 (d) 9450
24. 24.What is the smallest number you must add to 819 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 807 so that it divides exactly by 7?
26. 26.What is the smallest number you must take away from 744 so that it divides exactly by 13?
27. 27.How many factors does 31 have?
28. 28.What is the smallest number you must add to 662 so that it divides exactly by 6?
29. 29.Which of these numbers divides exactly by 11? (a) 3943 (b) 2376 (c) 1692 (d) 1838
30. 30.Which of these numbers divides exactly by 9? (a) 8854 (b) 2780 (c) 1827 (d) 3477
31. 31.Which of these numbers divides exactly by 4? (a) 6889 (b) 2542 (c) 2098 (d) 3452
32. 32.Which of these numbers divides exactly by 6? (a) 9049 (b) 8200 (c) 3856 (d) 9324
33. 33.How many factors does 62 have?
34. 34.What is the smallest number you must add to 548 so that it divides exactly by 3?
35. 35.Which of these numbers divides exactly by 8? (a) 4385 (b) 8232 (c) 2908 (d) 2277
36. 36.What is the smallest number you must add to 191 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 868 so that it divides exactly by 9?
38. 38.What is the smallest number you must take away from 724 so that it divides exactly by 8?
39. 39.What is the smallest number you must add to 447 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 207 so that it divides exactly by 7?

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