Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 218 · 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.How many factors does 91 have?
2. 2.What is the smallest number you must take away from 200 so that it divides exactly by 6?
3. 3.How many factors does 96 have?
4. 4.What is the smallest number you must add to 615 so that it divides exactly by 6?
5. 5.Which of these numbers divides exactly by 9? (a) 8174 (b) 8258 (c) 9639 (d) 7720
6. 6.What is the smallest number you must add to 953 so that it divides exactly by 6?
7. 7.Which of these numbers divides exactly by 6? (a) 7643 (b) 6600 (c) 1472 (d) 1226
8. 8.What is the smallest number you must add to 482 so that it divides exactly by 6?
9. 9.How many factors does 81 have?
10. 10.What is the smallest number you must add to 907 so that it divides exactly by 4?
11. 11.What is the smallest number you must add to 268 so that it divides exactly by 3?
12. 12.How many factors does 88 have?
13. 13.Which of these numbers divides exactly by 8? (a) 5261 (b) 2112 (c) 7210 (d) 4508
14. 14.Which of these numbers divides exactly by 9? (a) 6945 (b) 4329 (c) 9245 (d) 8907
15. 15.Which of these numbers divides exactly by 11? (a) 5280 (b) 8841 (c) 5218 (d) 9200
16. 16.What is the smallest number you must take away from 360 so that it divides exactly by 13?
17. 17.What is the smallest number you must add to 205 so that it divides exactly by 13?
18. 18.Which of these numbers divides exactly by 4? (a) 5920 (b) 4482 (c) 7123 (d) 1169
19. 19.How many factors does 83 have?
20. 20.Which of these numbers divides exactly by 4? (a) 8857 (b) 9111 (c) 3488 (d) 3351
21. 21.How many factors does 46 have?
22. 22.What is the smallest number you must take away from 617 so that it divides exactly by 12?
23. 23.What is the smallest number you must take away from 241 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 11? (a) 8969 (b) 6555 (c) 4346 (d) 7777
25. 25.Which of these numbers divides exactly by 3? (a) 8510 (b) 7157 (c) 6179 (d) 7818
26. 26.What is the smallest number you must take away from 424 so that it divides exactly by 6?
27. 27.How many factors does 94 have?
28. 28.Which of these numbers divides exactly by 11? (a) 3972 (b) 4108 (c) 1741 (d) 8800
29. 29.How many factors does 52 have?
30. 30.What is the smallest number you must take away from 589 so that it divides exactly by 13?
31. 31.What is the smallest number you must add to 413 so that it divides exactly by 13?
32. 32.Which of these numbers divides exactly by 3? (a) 1251 (b) 1481 (c) 6547 (d) 5081
33. 33.Which of these numbers divides exactly by 8? (a) 9665 (b) 8718 (c) 5912 (d) 6782
34. 34.Which of these numbers divides exactly by 3? (a) 2880 (b) 3848 (c) 9212 (d) 2669
35. 35.What is the smallest number you must take away from 545 so that it divides exactly by 11?
36. 36.How many factors does 64 have?
37. 37.How many factors does 22 have?
38. 38.How many factors does 20 have?
39. 39.Which of these numbers divides exactly by 11? (a) 4388 (b) 8375 (c) 2053 (d) 4730
40. 40.How many factors does 16 have?

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