Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 293 · 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.What is the smallest number you must take away from 315 so that it divides exactly by 6?
2. 2.What is the smallest number you must add to 741 so that it divides exactly by 4?
3. 3.How many factors does 61 have?
4. 4.How many factors does 64 have?
5. 5.What is the smallest number you must take away from 576 so that it divides exactly by 11?
6. 6.Which of these numbers divides exactly by 3? (a) 8449 (b) 7613 (c) 3671 (d) 7941
7. 7.What is the smallest number you must add to 982 so that it divides exactly by 13?
8. 8.What is the smallest number you must take away from 139 so that it divides exactly by 12?
9. 9.How many factors does 40 have?
10. 10.What is the smallest number you must add to 710 so that it divides exactly by 3?
11. 11.How many factors does 26 have?
12. 12.How many factors does 37 have?
13. 13.Which of these numbers divides exactly by 11? (a) 1683 (b) 1128 (c) 8916 (d) 1266
14. 14.Which of these numbers divides exactly by 6? (a) 5790 (b) 9082 (c) 4427 (d) 7589
15. 15.What is the smallest number you must add to 858 so that it divides exactly by 4?
16. 16.How many factors does 62 have?
17. 17.What is the smallest number you must add to 179 so that it divides exactly by 9?
18. 18.How many factors does 48 have?
19. 19.Which of these numbers divides exactly by 4? (a) 5351 (b) 1812 (c) 5773 (d) 1521
20. 20.What is the smallest number you must add to 557 so that it divides exactly by 12?
21. 21.How many factors does 27 have?
22. 22.Which of these numbers divides exactly by 9? (a) 3366 (b) 1187 (c) 9508 (d) 9988
23. 23.What is the smallest number you must take away from 402 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 11? (a) 2547 (b) 3184 (c) 6105 (d) 1273
25. 25.How many factors does 86 have?
26. 26.Which of these numbers divides exactly by 3? (a) 5824 (b) 6202 (c) 5765 (d) 1767
27. 27.What is the smallest number you must take away from 608 so that it divides exactly by 13?
28. 28.What is the smallest number you must take away from 582 so that it divides exactly by 4?
29. 29.What is the smallest number you must take away from 128 so that it divides exactly by 12?
30. 30.Which of these numbers divides exactly by 6? (a) 1718 (b) 3659 (c) 2814 (d) 5656
31. 31.Which of these numbers divides exactly by 11? (a) 7330 (b) 1215 (c) 4101 (d) 4147
32. 32.Which of these numbers divides exactly by 11? (a) 4572 (b) 2021 (c) 1796 (d) 3850
33. 33.Which of these numbers divides exactly by 4? (a) 2896 (b) 9429 (c) 9754 (d) 6990
34. 34.What is the smallest number you must add to 448 so that it divides exactly by 12?
35. 35.What is the smallest number you must add to 365 so that it divides exactly by 9?
36. 36.What is the smallest number you must add to 286 so that it divides exactly by 9?
37. 37.Which of these numbers divides exactly by 6? (a) 9465 (b) 8799 (c) 1236 (d) 8717
38. 38.How many factors does 72 have?
39. 39.What is the smallest number you must add to 610 so that it divides exactly by 8?
40. 40.Which of these numbers divides exactly by 3? (a) 2242 (b) 5829 (c) 1417 (d) 4088

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