Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 136 · 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.Which of these numbers divides exactly by 6? (a) 9862 (b) 5575 (c) 8478 (d) 2000
2. 2.How many factors does 94 have?
3. 3.How many factors does 49 have?
4. 4.What is the smallest number you must take away from 433 so that it divides exactly by 11?
5. 5.How many factors does 66 have?
6. 6.What is the smallest number you must take away from 101 so that it divides exactly by 3?
7. 7.What is the smallest number you must take away from 699 so that it divides exactly by 4?
8. 8.Which of these numbers divides exactly by 8? (a) 7760 (b) 3374 (c) 5859 (d) 5774
9. 9.Which of these numbers divides exactly by 8? (a) 9072 (b) 7341 (c) 2763 (d) 3007
10. 10.What is the smallest number you must add to 624 so that it divides exactly by 11?
11. 11.How many factors does 50 have?
12. 12.How many factors does 13 have?
13. 13.How many factors does 37 have?
14. 14.What is the smallest number you must take away from 415 so that it divides exactly by 12?
15. 15.How many factors does 89 have?
16. 16.What is the smallest number you must take away from 434 so that it divides exactly by 11?
17. 17.How many factors does 76 have?
18. 18.Which of these numbers divides exactly by 9? (a) 6891 (b) 9050 (c) 3800 (d) 7182
19. 19.What is the smallest number you must add to 269 so that it divides exactly by 3?
20. 20.Which of these numbers divides exactly by 3? (a) 7726 (b) 1052 (c) 4686 (d) 9553
21. 21.How many factors does 44 have?
22. 22.How many factors does 17 have?
23. 23.Which of these numbers divides exactly by 6? (a) 3031 (b) 8262 (c) 6700 (d) 2667
24. 24.What is the smallest number you must take away from 706 so that it divides exactly by 7?
25. 25.How many factors does 38 have?
26. 26.What is the smallest number you must add to 266 so that it divides exactly by 4?
27. 27.How many factors does 42 have?
28. 28.Which of these numbers divides exactly by 3? (a) 6868 (b) 3250 (c) 3450 (d) 1927
29. 29.How many factors does 69 have?
30. 30.What is the smallest number you must add to 509 so that it divides exactly by 12?
31. 31.What is the smallest number you must take away from 151 so that it divides exactly by 11?
32. 32.Which of these numbers divides exactly by 6? (a) 5019 (b) 8452 (c) 1900 (d) 7284
33. 33.What is the smallest number you must add to 650 so that it divides exactly by 4?
34. 34.Which of these numbers divides exactly by 11? (a) 2233 (b) 4503 (c) 7658 (d) 3965
35. 35.What is the smallest number you must take away from 116 so that it divides exactly by 7?
36. 36.What is the smallest number you must take away from 723 so that it divides exactly by 6?
37. 37.What is the smallest number you must take away from 823 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 226 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 132 so that it divides exactly by 13?
40. 40.What is the smallest number you must add to 401 so that it divides exactly by 11?

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