Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 318 · 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.Which of these numbers divides exactly by 8? (a) 5481 (b) 8855 (c) 4317 (d) 4904
2. 2.Which of these numbers divides exactly by 9? (a) 3509 (b) 7129 (c) 3895 (d) 3609
3. 3.How many factors does 89 have?
4. 4.How many factors does 27 have?
5. 5.How many factors does 86 have?
6. 6.What is the smallest number you must add to 279 so that it divides exactly by 4?
7. 7.How many factors does 15 have?
8. 8.What is the smallest number you must add to 499 so that it divides exactly by 6?
9. 9.What is the smallest number you must take away from 163 so that it divides exactly by 6?
10. 10.What is the smallest number you must take away from 998 so that it divides exactly by 4?
11. 11.What is the smallest number you must add to 555 so that it divides exactly by 13?
12. 12.How many factors does 87 have?
13. 13.Which of these numbers divides exactly by 6? (a) 6460 (b) 3774 (c) 3970 (d) 4081
14. 14.What is the smallest number you must take away from 221 so that it divides exactly by 4?
15. 15.How many factors does 69 have?
16. 16.How many factors does 53 have?
17. 17.What is the smallest number you must take away from 157 so that it divides exactly by 13?
18. 18.Which of these numbers divides exactly by 3? (a) 5164 (b) 9361 (c) 3854 (d) 1527
19. 19.How many factors does 58 have?
20. 20.What is the smallest number you must add to 657 so that it divides exactly by 13?
21. 21.Which of these numbers divides exactly by 4? (a) 1855 (b) 5468 (c) 9186 (d) 6799
22. 22.Which of these numbers divides exactly by 3? (a) 4657 (b) 5802 (c) 7724 (d) 7294
23. 23.What is the smallest number you must add to 550 so that it divides exactly by 8?
24. 24.What is the smallest number you must take away from 334 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 686 so that it divides exactly by 12?
26. 26.What is the smallest number you must add to 507 so that it divides exactly by 11?
27. 27.Which of these numbers divides exactly by 3? (a) 5124 (b) 3211 (c) 5833 (d) 7832
28. 28.How many factors does 16 have?
29. 29.What is the smallest number you must take away from 759 so that it divides exactly by 4?
30. 30.How many factors does 20 have?
31. 31.What is the smallest number you must add to 827 so that it divides exactly by 3?
32. 32.How many factors does 30 have?
33. 33.Which of these numbers divides exactly by 8? (a) 7072 (b) 2981 (c) 8687 (d) 7609
34. 34.How many factors does 94 have?
35. 35.What is the smallest number you must add to 721 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 833 so that it divides exactly by 11?
37. 37.What is the smallest number you must take away from 254 so that it divides exactly by 12?
38. 38.What is the smallest number you must add to 570 so that it divides exactly by 8?
39. 39.What is the smallest number you must add to 689 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 570 so that it divides exactly by 7?

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