Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 242 · 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 add to 251 so that it divides exactly by 7?
2. 2.Which of these numbers divides exactly by 11? (a) 5249 (b) 1111 (c) 3397 (d) 4303
3. 3.How many factors does 74 have?
4. 4.How many factors does 19 have?
5. 5.How many factors does 93 have?
6. 6.What is the smallest number you must add to 560 so that it divides exactly by 3?
7. 7.How many factors does 83 have?
8. 8.What is the smallest number you must add to 548 so that it divides exactly by 3?
9. 9.Which of these numbers divides exactly by 4? (a) 4041 (b) 4180 (c) 5113 (d) 2735
10. 10.What is the smallest number you must take away from 993 so that it divides exactly by 4?
11. 11.How many factors does 35 have?
12. 12.What is the smallest number you must take away from 743 so that it divides exactly by 7?
13. 13.What is the smallest number you must take away from 430 so that it divides exactly by 9?
14. 14.How many factors does 89 have?
15. 15.Which of these numbers divides exactly by 3? (a) 3924 (b) 5866 (c) 9859 (d) 8081
16. 16.Which of these numbers divides exactly by 3? (a) 2575 (b) 4118 (c) 1932 (d) 3805
17. 17.What is the smallest number you must take away from 417 so that it divides exactly by 13?
18. 18.How many factors does 80 have?
19. 19.What is the smallest number you must take away from 236 so that it divides exactly by 12?
20. 20.How many factors does 97 have?
21. 21.What is the smallest number you must add to 978 so that it divides exactly by 12?
22. 22.Which of these numbers divides exactly by 9? (a) 5022 (b) 7557 (c) 1876 (d) 1401
23. 23.What is the smallest number you must take away from 242 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 8? (a) 8028 (b) 1428 (c) 4416 (d) 8246
25. 25.How many factors does 56 have?
26. 26.What is the smallest number you must add to 402 so that it divides exactly by 8?
27. 27.What is the smallest number you must take away from 346 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 780 so that it divides exactly by 9?
29. 29.Which of these numbers divides exactly by 3? (a) 4724 (b) 3095 (c) 2644 (d) 4686
30. 30.What is the smallest number you must add to 967 so that it divides exactly by 4?
31. 31.Which of these numbers divides exactly by 4? (a) 6012 (b) 8449 (c) 6934 (d) 3455
32. 32.What is the smallest number you must take away from 609 so that it divides exactly by 4?
33. 33.Which of these numbers divides exactly by 11? (a) 1697 (b) 5730 (c) 1970 (d) 3124
34. 34.What is the smallest number you must take away from 845 so that it divides exactly by 4?
35. 35.What is the smallest number you must add to 227 so that it divides exactly by 9?
36. 36.What is the smallest number you must add to 202 so that it divides exactly by 6?
37. 37.What is the smallest number you must add to 128 so that it divides exactly by 7?
38. 38.What is the smallest number you must take away from 875 so that it divides exactly by 11?
39. 39.How many factors does 25 have?
40. 40.Which of these numbers divides exactly by 3? (a) 1494 (b) 5156 (c) 1762 (d) 2815

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