Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 203 · 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 657 so that it divides exactly by 4?
2. 2.What is the smallest number you must add to 889 so that it divides exactly by 12?
3. 3.What is the smallest number you must take away from 110 so that it divides exactly by 6?
4. 4.What is the smallest number you must take away from 905 so that it divides exactly by 4?
5. 5.How many factors does 53 have?
6. 6.Which of these numbers divides exactly by 3? (a) 7196 (b) 2900 (c) 8018 (d) 1020
7. 7.What is the smallest number you must add to 509 so that it divides exactly by 13?
8. 8.What is the smallest number you must take away from 622 so that it divides exactly by 12?
9. 9.What is the smallest number you must take away from 911 so that it divides exactly by 12?
10. 10.How many factors does 13 have?
11. 11.What is the smallest number you must take away from 956 so that it divides exactly by 8?
12. 12.How many factors does 87 have?
13. 13.What is the smallest number you must take away from 738 so that it divides exactly by 7?
14. 14.Which of these numbers divides exactly by 8? (a) 6411 (b) 7472 (c) 1563 (d) 7106
15. 15.What is the smallest number you must take away from 353 so that it divides exactly by 8?
16. 16.How many factors does 40 have?
17. 17.How many factors does 51 have?
18. 18.What is the smallest number you must add to 818 so that it divides exactly by 3?
19. 19.Which of these numbers divides exactly by 6? (a) 7128 (b) 4677 (c) 8000 (d) 9135
20. 20.Which of these numbers divides exactly by 11? (a) 4049 (b) 4130 (c) 9809 (d) 3696
21. 21.Which of these numbers divides exactly by 4? (a) 6046 (b) 2843 (c) 5226 (d) 8456
22. 22.How many factors does 47 have?
23. 23.How many factors does 61 have?
24. 24.How many factors does 49 have?
25. 25.How many factors does 25 have?
26. 26.What is the smallest number you must take away from 755 so that it divides exactly by 12?
27. 27.How many factors does 31 have?
28. 28.What is the smallest number you must take away from 676 so that it divides exactly by 9?
29. 29.How many factors does 67 have?
30. 30.What is the smallest number you must add to 724 so that it divides exactly by 6?
31. 31.Which of these numbers divides exactly by 11? (a) 1790 (b) 5016 (c) 4271 (d) 2578
32. 32.What is the smallest number you must add to 757 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 215 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 804 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 4? (a) 9069 (b) 9223 (c) 7004 (d) 6146
36. 36.How many factors does 90 have?
37. 37.What is the smallest number you must add to 736 so that it divides exactly by 13?
38. 38.What is the smallest number you must add to 666 so that it divides exactly by 4?
39. 39.What is the smallest number you must take away from 356 so that it divides exactly by 11?
40. 40.What is the smallest number you must take away from 950 so that it divides exactly by 7?

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