Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 325 · 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 3? (a) 9619 (b) 5806 (c) 1368 (d) 7097
2. 2.Which of these numbers divides exactly by 3? (a) 4188 (b) 1219 (c) 5605 (d) 7441
3. 3.What is the smallest number you must add to 717 so that it divides exactly by 6?
4. 4.How many factors does 91 have?
5. 5.How many factors does 23 have?
6. 6.Which of these numbers divides exactly by 8? (a) 4244 (b) 3574 (c) 3037 (d) 1704
7. 7.What is the smallest number you must take away from 622 so that it divides exactly by 3?
8. 8.What is the smallest number you must add to 876 so that it divides exactly by 13?
9. 9.How many factors does 19 have?
10. 10.How many factors does 22 have?
11. 11.Which of these numbers divides exactly by 8? (a) 1021 (b) 5504 (c) 6277 (d) 4149
12. 12.What is the smallest number you must take away from 113 so that it divides exactly by 8?
13. 13.How many factors does 84 have?
14. 14.What is the smallest number you must take away from 360 so that it divides exactly by 11?
15. 15.Which of these numbers divides exactly by 8? (a) 5687 (b) 8525 (c) 4672 (d) 8799
16. 16.How many factors does 27 have?
17. 17.How many factors does 98 have?
18. 18.What is the smallest number you must take away from 812 so that it divides exactly by 12?
19. 19.What is the smallest number you must add to 424 so that it divides exactly by 12?
20. 20.How many factors does 87 have?
21. 21.What is the smallest number you must take away from 164 so that it divides exactly by 9?
22. 22.Which of these numbers divides exactly by 8? (a) 5187 (b) 1364 (c) 6488 (d) 6753
23. 23.What is the smallest number you must add to 404 so that it divides exactly by 9?
24. 24.What is the smallest number you must add to 590 so that it divides exactly by 3?
25. 25.How many factors does 33 have?
26. 26.What is the smallest number you must add to 775 so that it divides exactly by 4?
27. 27.What is the smallest number you must take away from 306 so that it divides exactly by 4?
28. 28.What is the smallest number you must take away from 965 so that it divides exactly by 13?
29. 29.Which of these numbers divides exactly by 3? (a) 3994 (b) 3885 (c) 3433 (d) 1763
30. 30.What is the smallest number you must add to 584 so that it divides exactly by 12?
31. 31.What is the smallest number you must add to 250 so that it divides exactly by 7?
32. 32.Which of these numbers divides exactly by 11? (a) 6592 (b) 4037 (c) 6940 (d) 8742
33. 33.How many factors does 50 have?
34. 34.Which of these numbers divides exactly by 9? (a) 1779 (b) 1044 (c) 2893 (d) 3547
35. 35.How many factors does 46 have?
36. 36.How many factors does 40 have?
37. 37.What is the smallest number you must take away from 268 so that it divides exactly by 9?
38. 38.What is the smallest number you must take away from 469 so that it divides exactly by 11?
39. 39.What is the smallest number you must add to 135 so that it divides exactly by 4?
40. 40.What is the smallest number you must take away from 957 so that it divides exactly by 9?

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