Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 111 · 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 680 so that it divides exactly by 6?
2. 2.What is the smallest number you must add to 614 so that it divides exactly by 13?
3. 3.How many factors does 92 have?
4. 4.What is the smallest number you must take away from 209 so that it divides exactly by 8?
5. 5.Which of these numbers divides exactly by 8? (a) 4508 (b) 8247 (c) 6608 (d) 7226
6. 6.What is the smallest number you must add to 906 so that it divides exactly by 11?
7. 7.What is the smallest number you must add to 214 so that it divides exactly by 11?
8. 8.Which of these numbers divides exactly by 8? (a) 2503 (b) 8624 (c) 1049 (d) 1126
9. 9.How many factors does 44 have?
10. 10.How many factors does 72 have?
11. 11.What is the smallest number you must add to 355 so that it divides exactly by 6?
12. 12.How many factors does 12 have?
13. 13.How many factors does 33 have?
14. 14.Which of these numbers divides exactly by 4? (a) 5710 (b) 3562 (c) 6102 (d) 6948
15. 15.What is the smallest number you must add to 382 so that it divides exactly by 9?
16. 16.What is the smallest number you must add to 200 so that it divides exactly by 13?
17. 17.What is the smallest number you must take away from 912 so that it divides exactly by 9?
18. 18.What is the smallest number you must add to 645 so that it divides exactly by 9?
19. 19.What is the smallest number you must add to 177 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 610 so that it divides exactly by 8?
21. 21.Which of these numbers divides exactly by 11? (a) 5324 (b) 3240 (c) 6423 (d) 2348
22. 22.What is the smallest number you must take away from 766 so that it divides exactly by 13?
23. 23.What is the smallest number you must take away from 958 so that it divides exactly by 7?
24. 24.How many factors does 18 have?
25. 25.How many factors does 24 have?
26. 26.What is the smallest number you must take away from 170 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 148 so that it divides exactly by 12?
28. 28.Which of these numbers divides exactly by 3? (a) 7265 (b) 5419 (c) 5664 (d) 5747
29. 29.Which of these numbers divides exactly by 6? (a) 1018 (b) 6186 (c) 5329 (d) 9730
30. 30.How many factors does 89 have?
31. 31.What is the smallest number you must take away from 912 so that it divides exactly by 13?
32. 32.What is the smallest number you must take away from 289 so that it divides exactly by 9?
33. 33.What is the smallest number you must take away from 703 so that it divides exactly by 3?
34. 34.Which of these numbers divides exactly by 8? (a) 2118 (b) 4320 (c) 7746 (d) 8054
35. 35.How many factors does 52 have?
36. 36.Which of these numbers divides exactly by 3? (a) 5068 (b) 9076 (c) 9406 (d) 3840
37. 37.How many factors does 61 have?
38. 38.Which of these numbers divides exactly by 11? (a) 6353 (b) 8413 (c) 7517 (d) 4620
39. 39.How many factors does 45 have?
40. 40.What is the smallest number you must take away from 232 so that it divides exactly by 11?

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