Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 300 · 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 3? (a) 6302 (b) 9113 (c) 2988 (d) 4181
2. 2.What is the smallest number you must add to 165 so that it divides exactly by 9?
3. 3.What is the smallest number you must take away from 149 so that it divides exactly by 9?
4. 4.Which of these numbers divides exactly by 4? (a) 4889 (b) 2984 (c) 2039 (d) 8897
5. 5.How many factors does 25 have?
6. 6.Which of these numbers divides exactly by 3? (a) 6357 (b) 2530 (c) 8368 (d) 2347
7. 7.Which of these numbers divides exactly by 4? (a) 3855 (b) 4009 (c) 4797 (d) 5904
8. 8.How many factors does 57 have?
9. 9.Which of these numbers divides exactly by 4? (a) 4991 (b) 1594 (c) 1936 (d) 5137
10. 10.How many factors does 83 have?
11. 11.What is the smallest number you must add to 823 so that it divides exactly by 6?
12. 12.What is the smallest number you must take away from 673 so that it divides exactly by 4?
13. 13.How many factors does 82 have?
14. 14.What is the smallest number you must take away from 587 so that it divides exactly by 4?
15. 15.How many factors does 40 have?
16. 16.What is the smallest number you must take away from 153 so that it divides exactly by 6?
17. 17.What is the smallest number you must take away from 358 so that it divides exactly by 13?
18. 18.What is the smallest number you must take away from 827 so that it divides exactly by 6?
19. 19.What is the smallest number you must take away from 337 so that it divides exactly by 3?
20. 20.How many factors does 75 have?
21. 21.What is the smallest number you must add to 201 so that it divides exactly by 4?
22. 22.Which of these numbers divides exactly by 9? (a) 9740 (b) 6030 (c) 4205 (d) 6621
23. 23.Which of these numbers divides exactly by 9? (a) 9988 (b) 6545 (c) 7101 (d) 4097
24. 24.Which of these numbers divides exactly by 4? (a) 4152 (b) 2258 (c) 5023 (d) 5378
25. 25.Which of these numbers divides exactly by 11? (a) 6567 (b) 1552 (c) 3046 (d) 1810
26. 26.What is the smallest number you must take away from 657 so that it divides exactly by 6?
27. 27.What is the smallest number you must take away from 310 so that it divides exactly by 6?
28. 28.What is the smallest number you must take away from 317 so that it divides exactly by 8?
29. 29.How many factors does 48 have?
30. 30.What is the smallest number you must take away from 133 so that it divides exactly by 13?
31. 31.What is the smallest number you must add to 957 so that it divides exactly by 13?
32. 32.Which of these numbers divides exactly by 9? (a) 6753 (b) 8852 (c) 6117 (d) 9954
33. 33.Which of these numbers divides exactly by 6? (a) 8035 (b) 3031 (c) 3090 (d) 4653
34. 34.What is the smallest number you must add to 690 so that it divides exactly by 8?
35. 35.What is the smallest number you must take away from 577 so that it divides exactly by 8?
36. 36.Which of these numbers divides exactly by 3? (a) 3439 (b) 9207 (c) 1129 (d) 2921
37. 37.Which of these numbers divides exactly by 9? (a) 2268 (b) 2353 (c) 2860 (d) 9906
38. 38.Which of these numbers divides exactly by 3? (a) 9738 (b) 9976 (c) 9209 (d) 1396
39. 39.Which of these numbers divides exactly by 4? (a) 1166 (b) 1944 (c) 1365 (d) 2365
40. 40.How many factors does 23 have?

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