Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 104 · 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 845 so that it divides exactly by 4?
2. 2.Which of these numbers divides exactly by 8? (a) 4377 (b) 4758 (c) 1510 (d) 5880
3. 3.What is the smallest number you must add to 538 so that it divides exactly by 7?
4. 4.What is the smallest number you must take away from 195 so that it divides exactly by 6?
5. 5.What is the smallest number you must take away from 994 so that it divides exactly by 8?
6. 6.Which of these numbers divides exactly by 11? (a) 2374 (b) 5300 (c) 3179 (d) 6319
7. 7.How many factors does 97 have?
8. 8.What is the smallest number you must take away from 725 so that it divides exactly by 6?
9. 9.Which of these numbers divides exactly by 4? (a) 4408 (b) 3358 (c) 5689 (d) 7846
10. 10.What is the smallest number you must take away from 685 so that it divides exactly by 9?
11. 11.Which of these numbers divides exactly by 11? (a) 8473 (b) 3329 (c) 5912 (d) 7942
12. 12.Which of these numbers divides exactly by 6? (a) 7380 (b) 1456 (c) 1738 (d) 5684
13. 13.What is the smallest number you must add to 142 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 346 so that it divides exactly by 8?
15. 15.What is the smallest number you must take away from 993 so that it divides exactly by 6?
16. 16.What is the smallest number you must add to 836 so that it divides exactly by 12?
17. 17.What is the smallest number you must add to 328 so that it divides exactly by 12?
18. 18.What is the smallest number you must take away from 133 so that it divides exactly by 3?
19. 19.How many factors does 21 have?
20. 20.What is the smallest number you must take away from 410 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 910 so that it divides exactly by 3?
22. 22.Which of these numbers divides exactly by 11? (a) 5885 (b) 1325 (c) 5399 (d) 5435
23. 23.What is the smallest number you must add to 295 so that it divides exactly by 8?
24. 24.How many factors does 72 have?
25. 25.How many factors does 36 have?
26. 26.Which of these numbers divides exactly by 4? (a) 9720 (b) 1235 (c) 6915 (d) 6397
27. 27.How many factors does 82 have?
28. 28.What is the smallest number you must add to 464 so that it divides exactly by 7?
29. 29.How many factors does 15 have?
30. 30.Which of these numbers divides exactly by 4? (a) 2323 (b) 4164 (c) 4365 (d) 3062
31. 31.What is the smallest number you must add to 981 so that it divides exactly by 12?
32. 32.What is the smallest number you must take away from 352 so that it divides exactly by 3?
33. 33.How many factors does 22 have?
34. 34.How many factors does 84 have?
35. 35.What is the smallest number you must add to 706 so that it divides exactly by 11?
36. 36.How many factors does 91 have?
37. 37.What is the smallest number you must take away from 938 so that it divides exactly by 8?
38. 38.Which of these numbers divides exactly by 9? (a) 7134 (b) 1481 (c) 2862 (d) 3002
39. 39.What is the smallest number you must take away from 960 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 902 so that it divides exactly by 12?

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