Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 222 · 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 9? (a) 6373 (b) 1541 (c) 1219 (d) 3051
2. 2.How many factors does 71 have?
3. 3.Which of these numbers divides exactly by 4? (a) 6773 (b) 1284 (c) 7350 (d) 5685
4. 4.How many factors does 37 have?
5. 5.Which of these numbers divides exactly by 3? (a) 1922 (b) 1308 (c) 2302 (d) 6016
6. 6.Which of these numbers divides exactly by 9? (a) 8144 (b) 3902 (c) 2565 (d) 4719
7. 7.Which of these numbers divides exactly by 6? (a) 3600 (b) 7259 (c) 2966 (d) 7873
8. 8.What is the smallest number you must add to 614 so that it divides exactly by 6?
9. 9.Which of these numbers divides exactly by 6? (a) 9734 (b) 2957 (c) 7731 (d) 7662
10. 10.What is the smallest number you must take away from 237 so that it divides exactly by 7?
11. 11.How many factors does 94 have?
12. 12.What is the smallest number you must take away from 782 so that it divides exactly by 4?
13. 13.What is the smallest number you must add to 895 so that it divides exactly by 4?
14. 14.How many factors does 64 have?
15. 15.What is the smallest number you must take away from 963 so that it divides exactly by 4?
16. 16.Which of these numbers divides exactly by 3? (a) 9792 (b) 9104 (c) 3014 (d) 9913
17. 17.Which of these numbers divides exactly by 8? (a) 7899 (b) 1639 (c) 2704 (d) 4756
18. 18.How many factors does 34 have?
19. 19.Which of these numbers divides exactly by 4? (a) 3989 (b) 2204 (c) 9547 (d) 4003
20. 20.How many factors does 17 have?
21. 21.Which of these numbers divides exactly by 8? (a) 4634 (b) 1780 (c) 3784 (d) 2662
22. 22.Which of these numbers divides exactly by 3? (a) 8009 (b) 5829 (c) 9419 (d) 9133
23. 23.How many factors does 36 have?
24. 24.What is the smallest number you must take away from 352 so that it divides exactly by 12?
25. 25.Which of these numbers divides exactly by 6? (a) 3795 (b) 5079 (c) 8036 (d) 4716
26. 26.How many factors does 46 have?
27. 27.Which of these numbers divides exactly by 4? (a) 1195 (b) 4013 (c) 5730 (d) 5052
28. 28.How many factors does 35 have?
29. 29.Which of these numbers divides exactly by 4? (a) 4848 (b) 7701 (c) 6570 (d) 3881
30. 30.What is the smallest number you must add to 160 so that it divides exactly by 9?
31. 31.What is the smallest number you must add to 709 so that it divides exactly by 8?
32. 32.Which of these numbers divides exactly by 11? (a) 7568 (b) 9131 (c) 6199 (d) 5392
33. 33.Which of these numbers divides exactly by 3? (a) 2524 (b) 7109 (c) 8112 (d) 1664
34. 34.What is the smallest number you must take away from 724 so that it divides exactly by 6?
35. 35.How many factors does 12 have?
36. 36.How many factors does 93 have?
37. 37.What is the smallest number you must take away from 337 so that it divides exactly by 12?
38. 38.How many factors does 66 have?
39. 39.Which of these numbers divides exactly by 9? (a) 8721 (b) 3673 (c) 1855 (d) 2653
40. 40.Which of these numbers divides exactly by 9? (a) 2717 (b) 8631 (c) 5759 (d) 2701

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