Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 202 · 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 786 so that it divides exactly by 12?
2. 2.Which of these numbers divides exactly by 11? (a) 1529 (b) 6216 (c) 9993 (d) 1404
3. 3.What is the smallest number you must add to 709 so that it divides exactly by 3?
4. 4.What is the smallest number you must take away from 361 so that it divides exactly by 6?
5. 5.What is the smallest number you must add to 130 so that it divides exactly by 6?
6. 6.What is the smallest number you must add to 619 so that it divides exactly by 8?
7. 7.What is the smallest number you must add to 471 so that it divides exactly by 13?
8. 8.Which of these numbers divides exactly by 4? (a) 7520 (b) 1726 (c) 5421 (d) 9741
9. 9.What is the smallest number you must take away from 746 so that it divides exactly by 12?
10. 10.How many factors does 68 have?
11. 11.What is the smallest number you must take away from 181 so that it divides exactly by 7?
12. 12.How many factors does 51 have?
13. 13.How many factors does 82 have?
14. 14.What is the smallest number you must add to 269 so that it divides exactly by 11?
15. 15.What is the smallest number you must add to 757 so that it divides exactly by 4?
16. 16.What is the smallest number you must add to 667 so that it divides exactly by 12?
17. 17.What is the smallest number you must take away from 807 so that it divides exactly by 6?
18. 18.How many factors does 88 have?
19. 19.What is the smallest number you must take away from 158 so that it divides exactly by 11?
20. 20.What is the smallest number you must take away from 977 so that it divides exactly by 12?
21. 21.What is the smallest number you must take away from 687 so that it divides exactly by 6?
22. 22.What is the smallest number you must add to 574 so that it divides exactly by 4?
23. 23.Which of these numbers divides exactly by 11? (a) 2288 (b) 2070 (c) 5754 (d) 4553
24. 24.What is the smallest number you must take away from 118 so that it divides exactly by 9?
25. 25.What is the smallest number you must add to 500 so that it divides exactly by 3?
26. 26.What is the smallest number you must take away from 608 so that it divides exactly by 6?
27. 27.What is the smallest number you must add to 186 so that it divides exactly by 12?
28. 28.How many factors does 71 have?
29. 29.Which of these numbers divides exactly by 9? (a) 3215 (b) 6388 (c) 2952 (d) 9367
30. 30.Which of these numbers divides exactly by 4? (a) 6777 (b) 7386 (c) 3308 (d) 3129
31. 31.How many factors does 35 have?
32. 32.What is the smallest number you must add to 262 so that it divides exactly by 4?
33. 33.How many factors does 16 have?
34. 34.How many factors does 37 have?
35. 35.What is the smallest number you must add to 121 so that it divides exactly by 3?
36. 36.How many factors does 96 have?
37. 37.What is the smallest number you must add to 961 so that it divides exactly by 3?
38. 38.How many factors does 97 have?
39. 39.Which of these numbers divides exactly by 4? (a) 6717 (b) 6791 (c) 7798 (d) 8868
40. 40.What is the smallest number you must take away from 451 so that it divides exactly by 13?

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