Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 162 · 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) 5886 (b) 7835 (c) 3017 (d) 6566
2. 2.What is the smallest number you must add to 151 so that it divides exactly by 9?
3. 3.How many factors does 34 have?
4. 4.What is the smallest number you must take away from 820 so that it divides exactly by 13?
5. 5.Which of these numbers divides exactly by 11? (a) 3179 (b) 4937 (c) 4528 (d) 3845
6. 6.Which of these numbers divides exactly by 3? (a) 9920 (b) 2313 (c) 3664 (d) 9113
7. 7.How many factors does 14 have?
8. 8.What is the smallest number you must take away from 785 so that it divides exactly by 11?
9. 9.How many factors does 18 have?
10. 10.Which of these numbers divides exactly by 11? (a) 5852 (b) 1473 (c) 3236 (d) 1184
11. 11.How many factors does 70 have?
12. 12.What is the smallest number you must add to 241 so that it divides exactly by 4?
13. 13.What is the smallest number you must add to 925 so that it divides exactly by 13?
14. 14.Which of these numbers divides exactly by 9? (a) 4349 (b) 5934 (c) 2180 (d) 3015
15. 15.How many factors does 45 have?
16. 16.What is the smallest number you must add to 861 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 4? (a) 7265 (b) 9960 (c) 8079 (d) 8818
18. 18.What is the smallest number you must take away from 211 so that it divides exactly by 13?
19. 19.What is the smallest number you must add to 342 so that it divides exactly by 8?
20. 20.How many factors does 61 have?
21. 21.How many factors does 31 have?
22. 22.What is the smallest number you must take away from 386 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 706 so that it divides exactly by 7?
24. 24.What is the smallest number you must take away from 174 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 441 so that it divides exactly by 6?
26. 26.How many factors does 62 have?
27. 27.What is the smallest number you must take away from 921 so that it divides exactly by 6?
28. 28.What is the smallest number you must take away from 849 so that it divides exactly by 11?
29. 29.What is the smallest number you must take away from 582 so that it divides exactly by 11?
30. 30.What is the smallest number you must add to 193 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 9? (a) 2606 (b) 5723 (c) 4642 (d) 2232
32. 32.What is the smallest number you must add to 270 so that it divides exactly by 4?
33. 33.What is the smallest number you must take away from 458 so that it divides exactly by 9?
34. 34.How many factors does 35 have?
35. 35.How many factors does 32 have?
36. 36.What is the smallest number you must add to 738 so that it divides exactly by 4?
37. 37.Which of these numbers divides exactly by 4? (a) 5637 (b) 2118 (c) 6428 (d) 3021
38. 38.What is the smallest number you must add to 248 so that it divides exactly by 6?
39. 39.What is the smallest number you must add to 386 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 311 so that it divides exactly by 4?

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