Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 107 · 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 take away from 842 so that it divides exactly by 9?
2. 2.Which of these numbers divides exactly by 11? (a) 8337 (b) 1837 (c) 3360 (d) 5879
3. 3.What is the smallest number you must take away from 949 so that it divides exactly by 4?
4. 4.How many factors does 71 have?
5. 5.What is the smallest number you must take away from 601 so that it divides exactly by 8?
6. 6.Which of these numbers divides exactly by 8? (a) 5146 (b) 5886 (c) 7544 (d) 7613
7. 7.What is the smallest number you must add to 663 so that it divides exactly by 7?
8. 8.What is the smallest number you must take away from 250 so that it divides exactly by 8?
9. 9.What is the smallest number you must add to 184 so that it divides exactly by 9?
10. 10.What is the smallest number you must take away from 969 so that it divides exactly by 6?
11. 11.What is the smallest number you must add to 914 so that it divides exactly by 4?
12. 12.How many factors does 35 have?
13. 13.What is the smallest number you must take away from 589 so that it divides exactly by 6?
14. 14.What is the smallest number you must add to 953 so that it divides exactly by 6?
15. 15.Which of these numbers divides exactly by 8? (a) 1777 (b) 4083 (c) 2216 (d) 4962
16. 16.What is the smallest number you must add to 326 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 4? (a) 6266 (b) 7903 (c) 9084 (d) 2390
18. 18.How many factors does 98 have?
19. 19.What is the smallest number you must add to 700 so that it divides exactly by 3?
20. 20.Which of these numbers divides exactly by 4? (a) 2110 (b) 3420 (c) 1347 (d) 5834
21. 21.What is the smallest number you must take away from 117 so that it divides exactly by 11?
22. 22.What is the smallest number you must add to 374 so that it divides exactly by 6?
23. 23.Which of these numbers divides exactly by 3? (a) 4433 (b) 2009 (c) 3905 (d) 2031
24. 24.What is the smallest number you must take away from 908 so that it divides exactly by 13?
25. 25.What is the smallest number you must add to 921 so that it divides exactly by 6?
26. 26.What is the smallest number you must take away from 934 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 841 so that it divides exactly by 13?
28. 28.What is the smallest number you must take away from 854 so that it divides exactly by 4?
29. 29.What is the smallest number you must take away from 824 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 739 so that it divides exactly by 6?
31. 31.How many factors does 95 have?
32. 32.Which of these numbers divides exactly by 8? (a) 7239 (b) 6631 (c) 2408 (d) 2387
33. 33.What is the smallest number you must add to 553 so that it divides exactly by 9?
34. 34.How many factors does 53 have?
35. 35.What is the smallest number you must add to 270 so that it divides exactly by 8?
36. 36.What is the smallest number you must take away from 123 so that it divides exactly by 9?
37. 37.How many factors does 54 have?
38. 38.Which of these numbers divides exactly by 11? (a) 9388 (b) 8368 (c) 5643 (d) 3634
39. 39.How many factors does 63 have?
40. 40.How many factors does 37 have?

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