Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 43 · 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 660 so that it divides exactly by 8?
2. 2.Which of these numbers divides exactly by 4? (a) 9302 (b) 9260 (c) 9405 (d) 2969
3. 3.Which of these numbers divides exactly by 8? (a) 7397 (b) 6917 (c) 2226 (d) 6912
4. 4.Which of these numbers divides exactly by 11? (a) 4243 (b) 2958 (c) 3622 (d) 7634
5. 5.What is the smallest number you must add to 832 so that it divides exactly by 3?
6. 6.How many factors does 46 have?
7. 7.What is the smallest number you must add to 489 so that it divides exactly by 8?
8. 8.What is the smallest number you must add to 214 so that it divides exactly by 9?
9. 9.What is the smallest number you must add to 684 so that it divides exactly by 11?
10. 10.How many factors does 84 have?
11. 11.Which of these numbers divides exactly by 3? (a) 7806 (b) 3205 (c) 3652 (d) 6583
12. 12.What is the smallest number you must add to 222 so that it divides exactly by 4?
13. 13.How many factors does 67 have?
14. 14.What is the smallest number you must add to 712 so that it divides exactly by 7?
15. 15.How many factors does 28 have?
16. 16.What is the smallest number you must take away from 273 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 752 so that it divides exactly by 9?
18. 18.Which of these numbers divides exactly by 6? (a) 1694 (b) 5101 (c) 3617 (d) 7764
19. 19.How many factors does 21 have?
20. 20.How many factors does 38 have?
21. 21.What is the smallest number you must add to 333 so that it divides exactly by 12?
22. 22.What is the smallest number you must add to 878 so that it divides exactly by 13?
23. 23.How many factors does 63 have?
24. 24.How many factors does 68 have?
25. 25.How many factors does 78 have?
26. 26.How many factors does 20 have?
27. 27.How many factors does 27 have?
28. 28.Which of these numbers divides exactly by 9? (a) 7559 (b) 1666 (c) 6080 (d) 8487
29. 29.What is the smallest number you must add to 844 so that it divides exactly by 9?
30. 30.What is the smallest number you must add to 120 so that it divides exactly by 9?
31. 31.What is the smallest number you must add to 115 so that it divides exactly by 8?
32. 32.What is the smallest number you must add to 129 so that it divides exactly by 4?
33. 33.How many factors does 35 have?
34. 34.What is the smallest number you must take away from 869 so that it divides exactly by 13?
35. 35.What is the smallest number you must add to 259 so that it divides exactly by 9?
36. 36.What is the smallest number you must take away from 886 so that it divides exactly by 3?
37. 37.Which of these numbers divides exactly by 6? (a) 6355 (b) 1181 (c) 1800 (d) 3916
38. 38.What is the smallest number you must take away from 295 so that it divides exactly by 3?
39. 39.What is the smallest number you must take away from 809 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 640 so that it divides exactly by 12?

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