Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 5 · 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 17 have?
2. 2.What is the smallest number you must take away from 631 so that it divides exactly by 7?
3. 3.Which of these numbers divides exactly by 11? (a) 5098 (b) 6162 (c) 1747 (d) 5709
4. 4.What is the smallest number you must take away from 897 so that it divides exactly by 6?
5. 5.What is the smallest number you must add to 253 so that it divides exactly by 7?
6. 6.What is the smallest number you must add to 899 so that it divides exactly by 9?
7. 7.Which of these numbers divides exactly by 6? (a) 5107 (b) 2327 (c) 3216 (d) 5410
8. 8.What is the smallest number you must add to 862 so that it divides exactly by 4?
9. 9.How many factors does 33 have?
10. 10.Which of these numbers divides exactly by 9? (a) 8777 (b) 7487 (c) 3298 (d) 2439
11. 11.How many factors does 16 have?
12. 12.Which of these numbers divides exactly by 9? (a) 7629 (b) 3706 (c) 2880 (d) 5180
13. 13.What is the smallest number you must add to 221 so that it divides exactly by 12?
14. 14.How many factors does 95 have?
15. 15.Which of these numbers divides exactly by 11? (a) 1176 (b) 4651 (c) 3056 (d) 7865
16. 16.What is the smallest number you must add to 479 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 196 so that it divides exactly by 11?
18. 18.Which of these numbers divides exactly by 8? (a) 1528 (b) 9652 (c) 1545 (d) 4223
19. 19.How many factors does 58 have?
20. 20.How many factors does 39 have?
21. 21.What is the smallest number you must add to 682 so that it divides exactly by 13?
22. 22.Which of these numbers divides exactly by 9? (a) 8619 (b) 3218 (c) 6732 (d) 4017
23. 23.How many factors does 52 have?
24. 24.How many factors does 53 have?
25. 25.What is the smallest number you must take away from 481 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 3? (a) 5645 (b) 4809 (c) 5770 (d) 4193
27. 27.Which of these numbers divides exactly by 3? (a) 9946 (b) 9376 (c) 1518 (d) 2795
28. 28.Which of these numbers divides exactly by 4? (a) 9903 (b) 4072 (c) 9409 (d) 8859
29. 29.Which of these numbers divides exactly by 9? (a) 9637 (b) 2820 (c) 9368 (d) 1593
30. 30.Which of these numbers divides exactly by 8? (a) 2085 (b) 1857 (c) 4092 (d) 4656
31. 31.What is the smallest number you must take away from 776 so that it divides exactly by 12?
32. 32.Which of these numbers divides exactly by 4? (a) 7763 (b) 4689 (c) 2790 (d) 2148
33. 33.Which of these numbers divides exactly by 4? (a) 2836 (b) 7935 (c) 6233 (d) 3617
34. 34.What is the smallest number you must add to 881 so that it divides exactly by 11?
35. 35.How many factors does 69 have?
36. 36.Which of these numbers divides exactly by 8? (a) 1637 (b) 1595 (c) 5140 (d) 8208
37. 37.What is the smallest number you must take away from 782 so that it divides exactly by 7?
38. 38.How many factors does 82 have?
39. 39.What is the smallest number you must take away from 935 so that it divides exactly by 4?
40. 40.How many factors does 56 have?

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