Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 54 · 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 36 have?
2. 2.Which of these numbers divides exactly by 4? (a) 3203 (b) 1453 (c) 6468 (d) 7331
3. 3.Which of these numbers divides exactly by 3? (a) 2056 (b) 6484 (c) 3749 (d) 3540
4. 4.Which of these numbers divides exactly by 6? (a) 7829 (b) 7434 (c) 8066 (d) 9091
5. 5.Which of these numbers divides exactly by 9? (a) 7437 (b) 4931 (c) 4610 (d) 6606
6. 6.Which of these numbers divides exactly by 11? (a) 3525 (b) 8269 (c) 2736 (d) 2871
7. 7.How many factors does 92 have?
8. 8.How many factors does 86 have?
9. 9.What is the smallest number you must take away from 991 so that it divides exactly by 4?
10. 10.What is the smallest number you must take away from 595 so that it divides exactly by 12?
11. 11.How many factors does 14 have?
12. 12.How many factors does 56 have?
13. 13.What is the smallest number you must take away from 337 so that it divides exactly by 13?
14. 14.How many factors does 45 have?
15. 15.Which of these numbers divides exactly by 11? (a) 2263 (b) 2861 (c) 3630 (d) 9248
16. 16.What is the smallest number you must take away from 199 so that it divides exactly by 8?
17. 17.Which of these numbers divides exactly by 4? (a) 6101 (b) 7801 (c) 6624 (d) 8617
18. 18.How many factors does 85 have?
19. 19.What is the smallest number you must take away from 298 so that it divides exactly by 3?
20. 20.What is the smallest number you must take away from 833 so that it divides exactly by 8?
21. 21.How many factors does 15 have?
22. 22.What is the smallest number you must take away from 145 so that it divides exactly by 13?
23. 23.Which of these numbers divides exactly by 8? (a) 9518 (b) 2645 (c) 2909 (d) 5784
24. 24.What is the smallest number you must take away from 319 so that it divides exactly by 4?
25. 25.How many factors does 27 have?
26. 26.What is the smallest number you must add to 888 so that it divides exactly by 9?
27. 27.Which of these numbers divides exactly by 9? (a) 6313 (b) 1485 (c) 4588 (d) 5950
28. 28.What is the smallest number you must take away from 447 so that it divides exactly by 4?
29. 29.Which of these numbers divides exactly by 4? (a) 5077 (b) 3360 (c) 2366 (d) 4071
30. 30.What is the smallest number you must take away from 748 so that it divides exactly by 9?
31. 31.What is the smallest number you must take away from 217 so that it divides exactly by 3?
32. 32.Which of these numbers divides exactly by 8? (a) 6817 (b) 1415 (c) 8000 (d) 8508
33. 33.Which of these numbers divides exactly by 4? (a) 5534 (b) 9685 (c) 5179 (d) 8848
34. 34.How many factors does 41 have?
35. 35.How many factors does 82 have?
36. 36.What is the smallest number you must take away from 208 so that it divides exactly by 3?
37. 37.What is the smallest number you must add to 689 so that it divides exactly by 6?
38. 38.How many factors does 60 have?
39. 39.What is the smallest number you must add to 119 so that it divides exactly by 13?
40. 40.How many factors does 71 have?

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