Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 331 · 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 83 have?
2. 2.What is the smallest number you must add to 686 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 909 so that it divides exactly by 13?
4. 4.Which of these numbers divides exactly by 8? (a) 8441 (b) 8053 (c) 2477 (d) 7224
5. 5.How many factors does 25 have?
6. 6.What is the smallest number you must take away from 387 so that it divides exactly by 11?
7. 7.What is the smallest number you must add to 495 so that it divides exactly by 4?
8. 8.How many factors does 49 have?
9. 9.Which of these numbers divides exactly by 3? (a) 8071 (b) 1913 (c) 3939 (d) 6886
10. 10.What is the smallest number you must take away from 479 so that it divides exactly by 4?
11. 11.How many factors does 20 have?
12. 12.Which of these numbers divides exactly by 6? (a) 2674 (b) 8607 (c) 7693 (d) 1344
13. 13.What is the smallest number you must take away from 926 so that it divides exactly by 6?
14. 14.What is the smallest number you must take away from 334 so that it divides exactly by 4?
15. 15.What is the smallest number you must take away from 259 so that it divides exactly by 8?
16. 16.How many factors does 84 have?
17. 17.What is the smallest number you must add to 503 so that it divides exactly by 12?
18. 18.Which of these numbers divides exactly by 3? (a) 3099 (b) 5243 (c) 2123 (d) 8258
19. 19.How many factors does 29 have?
20. 20.Which of these numbers divides exactly by 3? (a) 1811 (b) 3081 (c) 9508 (d) 2746
21. 21.What is the smallest number you must take away from 667 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 681 so that it divides exactly by 8?
23. 23.How many factors does 45 have?
24. 24.How many factors does 82 have?
25. 25.What is the smallest number you must take away from 254 so that it divides exactly by 8?
26. 26.Which of these numbers divides exactly by 4? (a) 4230 (b) 1305 (c) 1436 (d) 6530
27. 27.What is the smallest number you must add to 801 so that it divides exactly by 4?
28. 28.What is the smallest number you must add to 817 so that it divides exactly by 3?
29. 29.Which of these numbers divides exactly by 8? (a) 3136 (b) 5165 (c) 7710 (d) 2899
30. 30.What is the smallest number you must take away from 327 so that it divides exactly by 8?
31. 31.Which of these numbers divides exactly by 6? (a) 9022 (b) 9057 (c) 8274 (d) 6710
32. 32.What is the smallest number you must add to 195 so that it divides exactly by 12?
33. 33.Which of these numbers divides exactly by 4? (a) 8493 (b) 2442 (c) 2516 (d) 7527
34. 34.What is the smallest number you must take away from 179 so that it divides exactly by 13?
35. 35.How many factors does 58 have?
36. 36.How many factors does 94 have?
37. 37.What is the smallest number you must add to 538 so that it divides exactly by 6?
38. 38.What is the smallest number you must take away from 239 so that it divides exactly by 11?
39. 39.How many factors does 33 have?
40. 40.How many factors does 78 have?

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