Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 14 · 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 82 have?
2. 2.What is the smallest number you must take away from 666 so that it divides exactly by 7?
3. 3.What is the smallest number you must take away from 605 so that it divides exactly by 13?
4. 4.Which of these numbers divides exactly by 4? (a) 8058 (b) 3449 (c) 3840 (d) 2085
5. 5.How many factors does 33 have?
6. 6.What is the smallest number you must add to 873 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 713 so that it divides exactly by 12?
8. 8.How many factors does 27 have?
9. 9.How many factors does 40 have?
10. 10.How many factors does 77 have?
11. 11.Which of these numbers divides exactly by 11? (a) 9218 (b) 4221 (c) 1390 (d) 2960
12. 12.What is the smallest number you must add to 521 so that it divides exactly by 11?
13. 13.How many factors does 31 have?
14. 14.How many factors does 28 have?
15. 15.What is the smallest number you must add to 137 so that it divides exactly by 3?
16. 16.Which of these numbers divides exactly by 4? (a) 8354 (b) 9908 (c) 5345 (d) 1811
17. 17.How many factors does 97 have?
18. 18.How many factors does 29 have?
19. 19.Which of these numbers divides exactly by 11? (a) 7699 (b) 5116 (c) 6410 (d) 7887
20. 20.Which of these numbers divides exactly by 3? (a) 7133 (b) 8060 (c) 1971 (d) 2153
21. 21.What is the smallest number you must add to 722 so that it divides exactly by 6?
22. 22.How many factors does 85 have?
23. 23.What is the smallest number you must take away from 608 so that it divides exactly by 3?
24. 24.Which of these numbers divides exactly by 3? (a) 9009 (b) 7411 (c) 5557 (d) 8554
25. 25.Which of these numbers divides exactly by 11? (a) 1577 (b) 3847 (c) 3226 (d) 1430
26. 26.How many factors does 12 have?
27. 27.Which of these numbers divides exactly by 11? (a) 8352 (b) 7792 (c) 2068 (d) 3194
28. 28.How many factors does 17 have?
29. 29.What is the smallest number you must add to 486 so that it divides exactly by 7?
30. 30.Which of these numbers divides exactly by 11? (a) 7062 (b) 4845 (c) 1740 (d) 7005
31. 31.Which of these numbers divides exactly by 8? (a) 2711 (b) 7720 (c) 1439 (d) 9619
32. 32.Which of these numbers divides exactly by 9? (a) 2142 (b) 8193 (c) 2283 (d) 1477
33. 33.Which of these numbers divides exactly by 8? (a) 1907 (b) 7049 (c) 3632 (d) 2305
34. 34.Which of these numbers divides exactly by 3? (a) 3755 (b) 8632 (c) 1579 (d) 7350
35. 35.What is the smallest number you must take away from 335 so that it divides exactly by 8?
36. 36.What is the smallest number you must add to 266 so that it divides exactly by 13?
37. 37.Which of these numbers divides exactly by 6? (a) 7150 (b) 7570 (c) 6308 (d) 3162
38. 38.What is the smallest number you must take away from 795 so that it divides exactly by 4?
39. 39.What is the smallest number you must take away from 338 so that it divides exactly by 9?
40. 40.What is the smallest number you must take away from 337 so that it divides exactly by 12?

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