Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 320 · 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.How many factors does 52 have?
2. 2.How many factors does 55 have?
3. 3.Which of these numbers divides exactly by 8? (a) 4634 (b) 7297 (c) 1920 (d) 4053
4. 4.What is the smallest number you must add to 606 so that it divides exactly by 12?
5. 5.Which of these numbers divides exactly by 9? (a) 9074 (b) 7506 (c) 6445 (d) 2473
6. 6.What is the smallest number you must take away from 223 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 6? (a) 5260 (b) 6670 (c) 4650 (d) 1694
8. 8.What is the smallest number you must add to 245 so that it divides exactly by 13?
9. 9.How many factors does 59 have?
10. 10.Which of these numbers divides exactly by 4? (a) 3190 (b) 1805 (c) 7464 (d) 7974
11. 11.Which of these numbers divides exactly by 4? (a) 2219 (b) 2299 (c) 8584 (d) 7261
12. 12.How many factors does 74 have?
13. 13.How many factors does 66 have?
14. 14.Which of these numbers divides exactly by 9? (a) 9482 (b) 2269 (c) 8685 (d) 6884
15. 15.How many factors does 19 have?
16. 16.What is the smallest number you must take away from 662 so that it divides exactly by 3?
17. 17.How many factors does 15 have?
18. 18.What is the smallest number you must take away from 342 so that it divides exactly by 4?
19. 19.What is the smallest number you must take away from 728 so that it divides exactly by 11?
20. 20.What is the smallest number you must take away from 637 so that it divides exactly by 8?
21. 21.What is the smallest number you must take away from 206 so that it divides exactly by 8?
22. 22.How many factors does 27 have?
23. 23.What is the smallest number you must take away from 482 so that it divides exactly by 11?
24. 24.What is the smallest number you must add to 129 so that it divides exactly by 4?
25. 25.What is the smallest number you must add to 914 so that it divides exactly by 13?
26. 26.How many factors does 95 have?
27. 27.How many factors does 48 have?
28. 28.What is the smallest number you must add to 323 so that it divides exactly by 13?
29. 29.Which of these numbers divides exactly by 6? (a) 9566 (b) 2222 (c) 3306 (d) 4154
30. 30.Which of these numbers divides exactly by 9? (a) 1114 (b) 8954 (c) 9702 (d) 1217
31. 31.How many factors does 23 have?
32. 32.What is the smallest number you must take away from 905 so that it divides exactly by 9?
33. 33.What is the smallest number you must add to 250 so that it divides exactly by 12?
34. 34.Which of these numbers divides exactly by 3? (a) 8931 (b) 4415 (c) 9403 (d) 2807
35. 35.What is the smallest number you must take away from 549 so that it divides exactly by 12?
36. 36.What is the smallest number you must take away from 154 so that it divides exactly by 6?
37. 37.What is the smallest number you must add to 186 so that it divides exactly by 12?
38. 38.What is the smallest number you must take away from 302 so that it divides exactly by 4?
39. 39.How many factors does 98 have?
40. 40.What is the smallest number you must take away from 872 so that it divides exactly by 9?

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