Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 198 · 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) 1640 (b) 2362 (c) 4005 (d) 2421
2. 2.How many factors does 65 have?
3. 3.What is the smallest number you must add to 381 so that it divides exactly by 12?
4. 4.What is the smallest number you must add to 434 so that it divides exactly by 3?
5. 5.What is the smallest number you must add to 632 so that it divides exactly by 13?
6. 6.What is the smallest number you must add to 211 so that it divides exactly by 9?
7. 7.What is the smallest number you must add to 385 so that it divides exactly by 8?
8. 8.What is the smallest number you must add to 454 so that it divides exactly by 8?
9. 9.How many factors does 13 have?
10. 10.What is the smallest number you must add to 255 so that it divides exactly by 13?
11. 11.What is the smallest number you must add to 788 so that it divides exactly by 3?
12. 12.What is the smallest number you must add to 331 so that it divides exactly by 9?
13. 13.What is the smallest number you must take away from 383 so that it divides exactly by 13?
14. 14.What is the smallest number you must add to 589 so that it divides exactly by 12?
15. 15.How many factors does 68 have?
16. 16.How many factors does 41 have?
17. 17.How many factors does 95 have?
18. 18.How many factors does 34 have?
19. 19.Which of these numbers divides exactly by 4? (a) 7057 (b) 1561 (c) 7020 (d) 6039
20. 20.What is the smallest number you must add to 981 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 913 so that it divides exactly by 7?
22. 22.Which of these numbers divides exactly by 11? (a) 5553 (b) 8735 (c) 3031 (d) 3872
23. 23.What is the smallest number you must add to 596 so that it divides exactly by 13?
24. 24.Which of these numbers divides exactly by 9? (a) 3377 (b) 8914 (c) 3744 (d) 8444
25. 25.What is the smallest number you must take away from 829 so that it divides exactly by 9?
26. 26.What is the smallest number you must add to 633 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 322 so that it divides exactly by 3?
28. 28.What is the smallest number you must add to 256 so that it divides exactly by 11?
29. 29.Which of these numbers divides exactly by 6? (a) 8774 (b) 2620 (c) 1107 (d) 7332
30. 30.Which of these numbers divides exactly by 6? (a) 2422 (b) 4782 (c) 1958 (d) 9704
31. 31.How many factors does 36 have?
32. 32.How many factors does 27 have?
33. 33.What is the smallest number you must add to 661 so that it divides exactly by 8?
34. 34.Which of these numbers divides exactly by 6? (a) 1257 (b) 8202 (c) 4430 (d) 8183
35. 35.What is the smallest number you must take away from 428 so that it divides exactly by 6?
36. 36.How many factors does 12 have?
37. 37.What is the smallest number you must add to 706 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 3? (a) 3175 (b) 1873 (c) 1596 (d) 3863
39. 39.How many factors does 66 have?
40. 40.What is the smallest number you must take away from 893 so that it divides exactly by 7?

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