Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 96 · 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 903 so that it divides exactly by 8?
2. 2.What is the smallest number you must take away from 815 so that it divides exactly by 11?
3. 3.What is the smallest number you must add to 866 so that it divides exactly by 8?
4. 4.Which of these numbers divides exactly by 3? (a) 2713 (b) 4394 (c) 1948 (d) 2313
5. 5.What is the smallest number you must add to 616 so that it divides exactly by 13?
6. 6.What is the smallest number you must take away from 228 so that it divides exactly by 13?
7. 7.What is the smallest number you must take away from 555 so that it divides exactly by 11?
8. 8.How many factors does 36 have?
9. 9.How many factors does 32 have?
10. 10.Which of these numbers divides exactly by 3? (a) 3430 (b) 2911 (c) 4336 (d) 8805
11. 11.What is the smallest number you must take away from 736 so that it divides exactly by 12?
12. 12.Which of these numbers divides exactly by 3? (a) 9256 (b) 4057 (c) 6269 (d) 6702
13. 13.What is the smallest number you must take away from 556 so that it divides exactly by 13?
14. 14.Which of these numbers divides exactly by 6? (a) 8753 (b) 7244 (c) 4377 (d) 2868
15. 15.What is the smallest number you must add to 493 so that it divides exactly by 11?
16. 16.What is the smallest number you must add to 950 so that it divides exactly by 3?
17. 17.Which of these numbers divides exactly by 11? (a) 4583 (b) 5517 (c) 4984 (d) 9438
18. 18.Which of these numbers divides exactly by 11? (a) 8693 (b) 2405 (c) 5379 (d) 7869
19. 19.What is the smallest number you must take away from 899 so that it divides exactly by 8?
20. 20.What is the smallest number you must add to 201 so that it divides exactly by 4?
21. 21.How many factors does 85 have?
22. 22.Which of these numbers divides exactly by 3? (a) 9620 (b) 4932 (c) 5632 (d) 7279
23. 23.Which of these numbers divides exactly by 3? (a) 2357 (b) 9789 (c) 2906 (d) 7370
24. 24.How many factors does 88 have?
25. 25.What is the smallest number you must take away from 383 so that it divides exactly by 12?
26. 26.How many factors does 16 have?
27. 27.How many factors does 41 have?
28. 28.How many factors does 97 have?
29. 29.Which of these numbers divides exactly by 8? (a) 9439 (b) 7486 (c) 7031 (d) 9952
30. 30.Which of these numbers divides exactly by 8? (a) 6108 (b) 7751 (c) 8150 (d) 3736
31. 31.What is the smallest number you must take away from 699 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 525 so that it divides exactly by 8?
33. 33.What is the smallest number you must add to 547 so that it divides exactly by 12?
34. 34.What is the smallest number you must add to 264 so that it divides exactly by 7?
35. 35.How many factors does 43 have?
36. 36.What is the smallest number you must add to 831 so that it divides exactly by 7?
37. 37.How many factors does 19 have?
38. 38.Which of these numbers divides exactly by 4? (a) 4321 (b) 3657 (c) 3316 (d) 9002
39. 39.What is the smallest number you must take away from 439 so that it divides exactly by 8?
40. 40.What is the smallest number you must add to 386 so that it divides exactly by 3?

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