Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 82 · 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 286 so that it divides exactly by 9?
2. 2.What is the smallest number you must take away from 149 so that it divides exactly by 3?
3. 3.Which of these numbers divides exactly by 4? (a) 7634 (b) 3326 (c) 4143 (d) 9060
4. 4.Which of these numbers divides exactly by 9? (a) 8094 (b) 9135 (c) 1039 (d) 3962
5. 5.How many factors does 68 have?
6. 6.How many factors does 90 have?
7. 7.Which of these numbers divides exactly by 4? (a) 5782 (b) 2624 (c) 3561 (d) 1979
8. 8.How many factors does 69 have?
9. 9.Which of these numbers divides exactly by 4? (a) 3462 (b) 5286 (c) 2448 (d) 2159
10. 10.What is the smallest number you must add to 986 so that it divides exactly by 12?
11. 11.Which of these numbers divides exactly by 9? (a) 3199 (b) 1060 (c) 7612 (d) 5625
12. 12.Which of these numbers divides exactly by 4? (a) 6953 (b) 8640 (c) 8829 (d) 8957
13. 13.Which of these numbers divides exactly by 11? (a) 2978 (b) 8147 (c) 4391 (d) 2354
14. 14.How many factors does 86 have?
15. 15.How many factors does 97 have?
16. 16.What is the smallest number you must take away from 187 so that it divides exactly by 13?
17. 17.What is the smallest number you must take away from 245 so that it divides exactly by 9?
18. 18.How many factors does 33 have?
19. 19.What is the smallest number you must add to 126 so that it divides exactly by 13?
20. 20.How many factors does 78 have?
21. 21.How many factors does 47 have?
22. 22.Which of these numbers divides exactly by 8? (a) 2172 (b) 1777 (c) 3333 (d) 1168
23. 23.What is the smallest number you must add to 499 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 982 so that it divides exactly by 9?
25. 25.How many factors does 21 have?
26. 26.What is the smallest number you must add to 976 so that it divides exactly by 3?
27. 27.What is the smallest number you must add to 161 so that it divides exactly by 4?
28. 28.Which of these numbers divides exactly by 3? (a) 2670 (b) 6733 (c) 2531 (d) 1787
29. 29.What is the smallest number you must take away from 691 so that it divides exactly by 7?
30. 30.Which of these numbers divides exactly by 8? (a) 8529 (b) 2625 (c) 1261 (d) 1768
31. 31.What is the smallest number you must add to 579 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 498 so that it divides exactly by 12?
33. 33.What is the smallest number you must take away from 243 so that it divides exactly by 7?
34. 34.Which of these numbers divides exactly by 8? (a) 5015 (b) 3063 (c) 8808 (d) 7785
35. 35.What is the smallest number you must add to 700 so that it divides exactly by 6?
36. 36.What is the smallest number you must add to 129 so that it divides exactly by 8?
37. 37.What is the smallest number you must take away from 376 so that it divides exactly by 11?
38. 38.Which of these numbers divides exactly by 8? (a) 3806 (b) 3452 (c) 4816 (d) 1012
39. 39.What is the smallest number you must add to 777 so that it divides exactly by 4?
40. 40.What is the smallest number you must add to 797 so that it divides exactly by 3?

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