Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 333 · 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 84 have?
2. 2.What is the smallest number you must take away from 961 so that it divides exactly by 13?
3. 3.What is the smallest number you must take away from 526 so that it divides exactly by 11?
4. 4.What is the smallest number you must take away from 601 so that it divides exactly by 4?
5. 5.What is the smallest number you must add to 662 so that it divides exactly by 4?
6. 6.How many factors does 70 have?
7. 7.What is the smallest number you must add to 565 so that it divides exactly by 4?
8. 8.How many factors does 98 have?
9. 9.What is the smallest number you must take away from 459 so that it divides exactly by 6?
10. 10.Which of these numbers divides exactly by 8? (a) 8015 (b) 8405 (c) 6488 (d) 6566
11. 11.What is the smallest number you must take away from 508 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 683 so that it divides exactly by 11?
13. 13.Which of these numbers divides exactly by 3? (a) 9290 (b) 9645 (c) 1168 (d) 1843
14. 14.What is the smallest number you must add to 489 so that it divides exactly by 13?
15. 15.What is the smallest number you must take away from 117 so that it divides exactly by 4?
16. 16.What is the smallest number you must take away from 311 so that it divides exactly by 3?
17. 17.Which of these numbers divides exactly by 8? (a) 6665 (b) 1597 (c) 2301 (d) 1248
18. 18.What is the smallest number you must add to 631 so that it divides exactly by 12?
19. 19.What is the smallest number you must add to 838 so that it divides exactly by 3?
20. 20.Which of these numbers divides exactly by 4? (a) 8361 (b) 4010 (c) 8609 (d) 7796
21. 21.Which of these numbers divides exactly by 3? (a) 9305 (b) 1229 (c) 1148 (d) 6654
22. 22.What is the smallest number you must take away from 912 so that it divides exactly by 9?
23. 23.What is the smallest number you must add to 640 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 224 so that it divides exactly by 3?
25. 25.Which of these numbers divides exactly by 6? (a) 6173 (b) 4734 (c) 2023 (d) 9577
26. 26.How many factors does 50 have?
27. 27.How many factors does 14 have?
28. 28.How many factors does 66 have?
29. 29.How many factors does 100 have?
30. 30.What is the smallest number you must add to 375 so that it divides exactly by 9?
31. 31.What is the smallest number you must add to 812 so that it divides exactly by 3?
32. 32.What is the smallest number you must add to 157 so that it divides exactly by 8?
33. 33.Which of these numbers divides exactly by 11? (a) 5209 (b) 5721 (c) 6567 (d) 3489
34. 34.What is the smallest number you must take away from 520 so that it divides exactly by 7?
35. 35.What is the smallest number you must add to 299 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 173 so that it divides exactly by 12?
37. 37.How many factors does 88 have?
38. 38.Which of these numbers divides exactly by 11? (a) 7865 (b) 5651 (c) 2363 (d) 2419
39. 39.What is the smallest number you must add to 457 so that it divides exactly by 4?
40. 40.How many factors does 21 have?

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