Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 214 · 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 4? (a) 5080 (b) 8783 (c) 2034 (d) 9335
2. 2.What is the smallest number you must take away from 340 so that it divides exactly by 12?
3. 3.Which of these numbers divides exactly by 8? (a) 8032 (b) 1426 (c) 8669 (d) 5669
4. 4.What is the smallest number you must add to 180 so that it divides exactly by 8?
5. 5.What is the smallest number you must add to 758 so that it divides exactly by 12?
6. 6.What is the smallest number you must take away from 862 so that it divides exactly by 6?
7. 7.Which of these numbers divides exactly by 3? (a) 3443 (b) 4301 (c) 4272 (d) 7634
8. 8.How many factors does 31 have?
9. 9.What is the smallest number you must add to 496 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 321 so that it divides exactly by 9?
11. 11.What is the smallest number you must take away from 242 so that it divides exactly by 13?
12. 12.Which of these numbers divides exactly by 4? (a) 5448 (b) 5075 (c) 4802 (d) 9463
13. 13.How many factors does 96 have?
14. 14.How many factors does 98 have?
15. 15.How many factors does 43 have?
16. 16.What is the smallest number you must take away from 405 so that it divides exactly by 8?
17. 17.Which of these numbers divides exactly by 4? (a) 1009 (b) 2303 (c) 2877 (d) 1568
18. 18.What is the smallest number you must add to 687 so that it divides exactly by 11?
19. 19.Which of these numbers divides exactly by 9? (a) 7861 (b) 1339 (c) 9954 (d) 7314
20. 20.What is the smallest number you must add to 737 so that it divides exactly by 9?
21. 21.How many factors does 64 have?
22. 22.What is the smallest number you must take away from 511 so that it divides exactly by 4?
23. 23.What is the smallest number you must add to 103 so that it divides exactly by 8?
24. 24.Which of these numbers divides exactly by 8? (a) 2175 (b) 7955 (c) 2016 (d) 8562
25. 25.How many factors does 41 have?
26. 26.Which of these numbers divides exactly by 4? (a) 5280 (b) 2022 (c) 5441 (d) 7435
27. 27.How many factors does 76 have?
28. 28.How many factors does 16 have?
29. 29.What is the smallest number you must add to 843 so that it divides exactly by 4?
30. 30.What is the smallest number you must add to 944 so that it divides exactly by 13?
31. 31.Which of these numbers divides exactly by 11? (a) 9218 (b) 6575 (c) 1889 (d) 2930
32. 32.What is the smallest number you must add to 494 so that it divides exactly by 8?
33. 33.What is the smallest number you must add to 598 so that it divides exactly by 12?
34. 34.What is the smallest number you must add to 548 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 3? (a) 4540 (b) 6239 (c) 8035 (d) 7872
36. 36.What is the smallest number you must add to 449 so that it divides exactly by 11?
37. 37.What is the smallest number you must add to 976 so that it divides exactly by 6?
38. 38.What is the smallest number you must add to 333 so that it divides exactly by 8?
39. 39.What is the smallest number you must take away from 586 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 691 so that it divides exactly by 13?

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