Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 84 · 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 531 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 460 so that it divides exactly by 9?
3. 3.What is the smallest number you must add to 348 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 8? (a) 6635 (b) 9302 (c) 9087 (d) 9064
5. 5.What is the smallest number you must take away from 547 so that it divides exactly by 3?
6. 6.How many factors does 24 have?
7. 7.How many factors does 21 have?
8. 8.What is the smallest number you must take away from 379 so that it divides exactly by 11?
9. 9.How many factors does 36 have?
10. 10.How many factors does 22 have?
11. 11.What is the smallest number you must take away from 320 so that it divides exactly by 13?
12. 12.Which of these numbers divides exactly by 11? (a) 1397 (b) 4010 (c) 7076 (d) 5711
13. 13.How many factors does 27 have?
14. 14.How many factors does 82 have?
15. 15.Which of these numbers divides exactly by 4? (a) 2566 (b) 4726 (c) 6120 (d) 4889
16. 16.What is the smallest number you must take away from 932 so that it divides exactly by 6?
17. 17.How many factors does 58 have?
18. 18.What is the smallest number you must take away from 925 so that it divides exactly by 4?
19. 19.How many factors does 18 have?
20. 20.What is the smallest number you must take away from 117 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 4? (a) 8105 (b) 2893 (c) 8033 (d) 1828
22. 22.Which of these numbers divides exactly by 4? (a) 7188 (b) 3487 (c) 6875 (d) 4251
23. 23.What is the smallest number you must take away from 523 so that it divides exactly by 3?
24. 24.What is the smallest number you must take away from 991 so that it divides exactly by 6?
25. 25.What is the smallest number you must take away from 155 so that it divides exactly by 7?
26. 26.How many factors does 19 have?
27. 27.How many factors does 46 have?
28. 28.What is the smallest number you must take away from 202 so that it divides exactly by 4?
29. 29.Which of these numbers divides exactly by 3? (a) 5473 (b) 7469 (c) 1541 (d) 3807
30. 30.What is the smallest number you must add to 751 so that it divides exactly by 12?
31. 31.What is the smallest number you must add to 165 so that it divides exactly by 12?
32. 32.What is the smallest number you must take away from 507 so that it divides exactly by 8?
33. 33.How many factors does 37 have?
34. 34.What is the smallest number you must take away from 243 so that it divides exactly by 12?
35. 35.Which of these numbers divides exactly by 11? (a) 9581 (b) 9842 (c) 4025 (d) 9967
36. 36.Which of these numbers divides exactly by 6? (a) 2957 (b) 2746 (c) 1542 (d) 1331
37. 37.What is the smallest number you must take away from 173 so that it divides exactly by 7?
38. 38.What is the smallest number you must add to 768 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 263 so that it divides exactly by 3?
40. 40.How many factors does 68 have?

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