Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 306 · 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 31 have?
2. 2.What is the smallest number you must add to 133 so that it divides exactly by 3?
3. 3.What is the smallest number you must add to 997 so that it divides exactly by 7?
4. 4.What is the smallest number you must add to 768 so that it divides exactly by 13?
5. 5.How many factors does 46 have?
6. 6.Which of these numbers divides exactly by 9? (a) 2411 (b) 8019 (c) 2822 (d) 8848
7. 7.Which of these numbers divides exactly by 3? (a) 5216 (b) 5049 (c) 7712 (d) 2239
8. 8.Which of these numbers divides exactly by 4? (a) 2315 (b) 3356 (c) 8038 (d) 5653
9. 9.What is the smallest number you must take away from 946 so that it divides exactly by 13?
10. 10.What is the smallest number you must take away from 604 so that it divides exactly by 3?
11. 11.Which of these numbers divides exactly by 3? (a) 6551 (b) 6284 (c) 4102 (d) 9501
12. 12.What is the smallest number you must take away from 485 so that it divides exactly by 6?
13. 13.What is the smallest number you must take away from 194 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 256 so that it divides exactly by 9?
15. 15.What is the smallest number you must add to 947 so that it divides exactly by 6?
16. 16.Which of these numbers divides exactly by 11? (a) 9436 (b) 9623 (c) 5060 (d) 5124
17. 17.What is the smallest number you must take away from 898 so that it divides exactly by 13?
18. 18.What is the smallest number you must add to 314 so that it divides exactly by 11?
19. 19.How many factors does 20 have?
20. 20.How many factors does 42 have?
21. 21.How many factors does 83 have?
22. 22.How many factors does 66 have?
23. 23.What is the smallest number you must take away from 825 so that it divides exactly by 9?
24. 24.What is the smallest number you must add to 569 so that it divides exactly by 13?
25. 25.How many factors does 29 have?
26. 26.Which of these numbers divides exactly by 3? (a) 4828 (b) 2302 (c) 7787 (d) 2247
27. 27.How many factors does 65 have?
28. 28.How many factors does 98 have?
29. 29.What is the smallest number you must take away from 515 so that it divides exactly by 7?
30. 30.Which of these numbers divides exactly by 9? (a) 1876 (b) 5163 (c) 9441 (d) 9944
31. 31.How many factors does 21 have?
32. 32.What is the smallest number you must take away from 241 so that it divides exactly by 7?
33. 33.How many factors does 62 have?
34. 34.What is the smallest number you must add to 490 so that it divides exactly by 9?
35. 35.What is the smallest number you must take away from 118 so that it divides exactly by 3?
36. 36.Which of these numbers divides exactly by 9? (a) 3442 (b) 1950 (c) 3346 (d) 2214
37. 37.What is the smallest number you must add to 539 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 11? (a) 8514 (b) 5480 (c) 3903 (d) 1645
39. 39.What is the smallest number you must add to 313 so that it divides exactly by 4?
40. 40.How many factors does 84 have?

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