Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 38 · 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 90 have?
2. 2.What is the smallest number you must add to 219 so that it divides exactly by 9?
3. 3.How many factors does 68 have?
4. 4.Which of these numbers divides exactly by 3? (a) 1196 (b) 7346 (c) 6968 (d) 5403
5. 5.What is the smallest number you must add to 570 so that it divides exactly by 11?
6. 6.What is the smallest number you must take away from 433 so that it divides exactly by 9?
7. 7.What is the smallest number you must take away from 146 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 879 so that it divides exactly by 13?
9. 9.What is the smallest number you must take away from 482 so that it divides exactly by 7?
10. 10.What is the smallest number you must add to 206 so that it divides exactly by 8?
11. 11.What is the smallest number you must add to 725 so that it divides exactly by 6?
12. 12.How many factors does 14 have?
13. 13.What is the smallest number you must take away from 989 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 202 so that it divides exactly by 7?
15. 15.How many factors does 95 have?
16. 16.What is the smallest number you must take away from 526 so that it divides exactly by 12?
17. 17.What is the smallest number you must take away from 917 so that it divides exactly by 13?
18. 18.Which of these numbers divides exactly by 9? (a) 7784 (b) 5398 (c) 1238 (d) 9873
19. 19.Which of these numbers divides exactly by 3? (a) 1475 (b) 4112 (c) 1392 (d) 7277
20. 20.What is the smallest number you must add to 296 so that it divides exactly by 12?
21. 21.How many factors does 18 have?
22. 22.What is the smallest number you must add to 757 so that it divides exactly by 4?
23. 23.Which of these numbers divides exactly by 3? (a) 3545 (b) 9918 (c) 4702 (d) 3263
24. 24.Which of these numbers divides exactly by 11? (a) 9455 (b) 8569 (c) 9353 (d) 5975
25. 25.Which of these numbers divides exactly by 11? (a) 2470 (b) 1980 (c) 1277 (d) 5408
26. 26.What is the smallest number you must take away from 946 so that it divides exactly by 3?
27. 27.What is the smallest number you must add to 475 so that it divides exactly by 7?
28. 28.How many factors does 32 have?
29. 29.Which of these numbers divides exactly by 4? (a) 7622 (b) 5467 (c) 7228 (d) 7413
30. 30.Which of these numbers divides exactly by 3? (a) 3836 (b) 4291 (c) 8339 (d) 2748
31. 31.What is the smallest number you must take away from 989 so that it divides exactly by 9?
32. 32.What is the smallest number you must add to 871 so that it divides exactly by 12?
33. 33.What is the smallest number you must add to 727 so that it divides exactly by 12?
34. 34.What is the smallest number you must add to 965 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 827 so that it divides exactly by 3?
36. 36.What is the smallest number you must add to 422 so that it divides exactly by 13?
37. 37.Which of these numbers divides exactly by 6? (a) 3002 (b) 6798 (c) 8787 (d) 9249
38. 38.What is the smallest number you must add to 229 so that it divides exactly by 6?
39. 39.Which of these numbers divides exactly by 3? (a) 6403 (b) 6061 (c) 4104 (d) 8609
40. 40.How many factors does 17 have?

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