Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 67 · 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 510 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 564 so that it divides exactly by 13?
3. 3.Which of these numbers divides exactly by 8? (a) 7641 (b) 6072 (c) 8501 (d) 4555
4. 4.Which of these numbers divides exactly by 11? (a) 5560 (b) 5632 (c) 2597 (d) 3232
5. 5.What is the smallest number you must take away from 587 so that it divides exactly by 9?
6. 6.What is the smallest number you must add to 833 so that it divides exactly by 3?
7. 7.How many factors does 79 have?
8. 8.What is the smallest number you must take away from 410 so that it divides exactly by 7?
9. 9.What is the smallest number you must add to 592 so that it divides exactly by 7?
10. 10.What is the smallest number you must take away from 593 so that it divides exactly by 6?
11. 11.How many factors does 96 have?
12. 12.What is the smallest number you must take away from 554 so that it divides exactly by 9?
13. 13.What is the smallest number you must add to 489 so that it divides exactly by 13?
14. 14.How many factors does 91 have?
15. 15.What is the smallest number you must take away from 609 so that it divides exactly by 4?
16. 16.Which of these numbers divides exactly by 9? (a) 6843 (b) 7602 (c) 9635 (d) 7857
17. 17.What is the smallest number you must take away from 915 so that it divides exactly by 11?
18. 18.Which of these numbers divides exactly by 9? (a) 4671 (b) 2893 (c) 2563 (d) 2064
19. 19.What is the smallest number you must take away from 418 so that it divides exactly by 13?
20. 20.Which of these numbers divides exactly by 4? (a) 3080 (b) 2978 (c) 8625 (d) 7099
21. 21.What is the smallest number you must add to 225 so that it divides exactly by 12?
22. 22.What is the smallest number you must take away from 721 so that it divides exactly by 3?
23. 23.What is the smallest number you must add to 856 so that it divides exactly by 12?
24. 24.How many factors does 24 have?
25. 25.Which of these numbers divides exactly by 8? (a) 8457 (b) 9575 (c) 9768 (d) 6975
26. 26.Which of these numbers divides exactly by 9? (a) 1642 (b) 7953 (c) 9081 (d) 8447
27. 27.What is the smallest number you must take away from 196 so that it divides exactly by 3?
28. 28.What is the smallest number you must take away from 646 so that it divides exactly by 11?
29. 29.How many factors does 65 have?
30. 30.Which of these numbers divides exactly by 3? (a) 7568 (b) 7987 (c) 1839 (d) 5642
31. 31.How many factors does 52 have?
32. 32.How many factors does 76 have?
33. 33.What is the smallest number you must add to 118 so that it divides exactly by 9?
34. 34.What is the smallest number you must take away from 683 so that it divides exactly by 9?
35. 35.What is the smallest number you must add to 822 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 341 so that it divides exactly by 6?
37. 37.What is the smallest number you must add to 335 so that it divides exactly by 6?
38. 38.What is the smallest number you must add to 218 so that it divides exactly by 11?
39. 39.What is the smallest number you must add to 200 so that it divides exactly by 11?
40. 40.Which of these numbers divides exactly by 8? (a) 2632 (b) 8305 (c) 5969 (d) 8327

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