Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 274 · 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 30 have?
2. 2.Which of these numbers divides exactly by 3? (a) 7714 (b) 1387 (c) 5705 (d) 1500
3. 3.Which of these numbers divides exactly by 9? (a) 3702 (b) 1640 (c) 1492 (d) 4221
4. 4.What is the smallest number you must add to 273 so that it divides exactly by 9?
5. 5.What is the smallest number you must take away from 899 so that it divides exactly by 9?
6. 6.What is the smallest number you must add to 147 so that it divides exactly by 6?
7. 7.What is the smallest number you must take away from 274 so that it divides exactly by 11?
8. 8.What is the smallest number you must add to 731 so that it divides exactly by 12?
9. 9.What is the smallest number you must take away from 772 so that it divides exactly by 8?
10. 10.Which of these numbers divides exactly by 3? (a) 1473 (b) 3439 (c) 8282 (d) 1513
11. 11.How many factors does 17 have?
12. 12.How many factors does 29 have?
13. 13.Which of these numbers divides exactly by 3? (a) 8905 (b) 8025 (c) 3403 (d) 2498
14. 14.Which of these numbers divides exactly by 8? (a) 4626 (b) 4466 (c) 5576 (d) 4364
15. 15.What is the smallest number you must add to 318 so that it divides exactly by 8?
16. 16.Which of these numbers divides exactly by 8? (a) 3134 (b) 2227 (c) 2568 (d) 4201
17. 17.What is the smallest number you must add to 839 so that it divides exactly by 6?
18. 18.What is the smallest number you must take away from 649 so that it divides exactly by 6?
19. 19.How many factors does 25 have?
20. 20.How many factors does 57 have?
21. 21.Which of these numbers divides exactly by 9? (a) 7895 (b) 9639 (c) 1552 (d) 5092
22. 22.What is the smallest number you must add to 967 so that it divides exactly by 3?
23. 23.Which of these numbers divides exactly by 4? (a) 8864 (b) 9450 (c) 1481 (d) 3058
24. 24.What is the smallest number you must take away from 390 so that it divides exactly by 8?
25. 25.What is the smallest number you must add to 580 so that it divides exactly by 12?
26. 26.Which of these numbers divides exactly by 11? (a) 2985 (b) 9065 (c) 9049 (d) 3410
27. 27.What is the smallest number you must add to 427 so that it divides exactly by 9?
28. 28.How many factors does 56 have?
29. 29.What is the smallest number you must take away from 690 so that it divides exactly by 4?
30. 30.How many factors does 97 have?
31. 31.What is the smallest number you must add to 249 so that it divides exactly by 12?
32. 32.What is the smallest number you must add to 417 so that it divides exactly by 12?
33. 33.Which of these numbers divides exactly by 6? (a) 2662 (b) 1986 (c) 5555 (d) 1687
34. 34.What is the smallest number you must add to 706 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 11? (a) 7720 (b) 2746 (c) 2775 (d) 1661
36. 36.What is the smallest number you must add to 605 so that it divides exactly by 8?
37. 37.How many factors does 68 have?
38. 38.What is the smallest number you must add to 610 so that it divides exactly by 6?
39. 39.Which of these numbers divides exactly by 11? (a) 5208 (b) 4730 (c) 7666 (d) 9808
40. 40.What is the smallest number you must add to 279 so that it divides exactly by 6?

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