Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 156 · 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 66 have?
2. 2.Which of these numbers divides exactly by 11? (a) 5303 (b) 7250 (c) 9873 (d) 1232
3. 3.What is the smallest number you must add to 211 so that it divides exactly by 3?
4. 4.What is the smallest number you must add to 131 so that it divides exactly by 13?
5. 5.How many factors does 47 have?
6. 6.Which of these numbers divides exactly by 3? (a) 8819 (b) 8522 (c) 8512 (d) 9480
7. 7.What is the smallest number you must take away from 189 so that it divides exactly by 12?
8. 8.Which of these numbers divides exactly by 4? (a) 3170 (b) 4846 (c) 9542 (d) 3432
9. 9.What is the smallest number you must add to 597 so that it divides exactly by 7?
10. 10.What is the smallest number you must take away from 883 so that it divides exactly by 13?
11. 11.Which of these numbers divides exactly by 8? (a) 3894 (b) 6128 (c) 8855 (d) 7133
12. 12.What is the smallest number you must take away from 790 so that it divides exactly by 6?
13. 13.Which of these numbers divides exactly by 11? (a) 2649 (b) 9449 (c) 8952 (d) 3255
14. 14.What is the smallest number you must take away from 202 so that it divides exactly by 12?
15. 15.How many factors does 14 have?
16. 16.Which of these numbers divides exactly by 6? (a) 8757 (b) 8905 (c) 2241 (d) 3960
17. 17.Which of these numbers divides exactly by 9? (a) 5440 (b) 9783 (c) 4532 (d) 6222
18. 18.How many factors does 15 have?
19. 19.What is the smallest number you must add to 914 so that it divides exactly by 13?
20. 20.Which of these numbers divides exactly by 3? (a) 3006 (b) 9682 (c) 1444 (d) 8615
21. 21.What is the smallest number you must take away from 613 so that it divides exactly by 8?
22. 22.How many factors does 57 have?
23. 23.What is the smallest number you must take away from 282 so that it divides exactly by 12?
24. 24.What is the smallest number you must add to 409 so that it divides exactly by 7?
25. 25.What is the smallest number you must add to 231 so that it divides exactly by 13?
26. 26.What is the smallest number you must take away from 116 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 233 so that it divides exactly by 4?
28. 28.How many factors does 37 have?
29. 29.Which of these numbers divides exactly by 6? (a) 6189 (b) 5646 (c) 2971 (d) 2687
30. 30.How many factors does 34 have?
31. 31.What is the smallest number you must add to 399 so that it divides exactly by 12?
32. 32.How many factors does 97 have?
33. 33.How many factors does 84 have?
34. 34.What is the smallest number you must take away from 164 so that it divides exactly by 3?
35. 35.What is the smallest number you must add to 125 so that it divides exactly by 3?
36. 36.What is the smallest number you must add to 459 so that it divides exactly by 7?
37. 37.Which of these numbers divides exactly by 6? (a) 9720 (b) 5729 (c) 5579 (d) 5935
38. 38.What is the smallest number you must take away from 743 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 8? (a) 3865 (b) 7952 (c) 4986 (d) 8909
40. 40.What is the smallest number you must take away from 679 so that it divides exactly by 12?

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