Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 246 · 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 121 so that it divides exactly by 7?
2. 2.What is the smallest number you must add to 567 so that it divides exactly by 8?
3. 3.Which of these numbers divides exactly by 11? (a) 3604 (b) 1477 (c) 3191 (d) 7733
4. 4.What is the smallest number you must add to 771 so that it divides exactly by 6?
5. 5.Which of these numbers divides exactly by 8? (a) 5344 (b) 5173 (c) 8071 (d) 6591
6. 6.Which of these numbers divides exactly by 8? (a) 4976 (b) 2410 (c) 9857 (d) 3373
7. 7.What is the smallest number you must add to 309 so that it divides exactly by 11?
8. 8.How many factors does 48 have?
9. 9.What is the smallest number you must add to 813 so that it divides exactly by 9?
10. 10.What is the smallest number you must add to 822 so that it divides exactly by 8?
11. 11.What is the smallest number you must add to 185 so that it divides exactly by 3?
12. 12.What is the smallest number you must take away from 707 so that it divides exactly by 6?
13. 13.What is the smallest number you must take away from 477 so that it divides exactly by 12?
14. 14.Which of these numbers divides exactly by 4? (a) 4375 (b) 4683 (c) 6680 (d) 3053
15. 15.What is the smallest number you must add to 795 so that it divides exactly by 4?
16. 16.How many factors does 90 have?
17. 17.How many factors does 22 have?
18. 18.Which of these numbers divides exactly by 4? (a) 4949 (b) 2186 (c) 1756 (d) 5702
19. 19.What is the smallest number you must add to 584 so that it divides exactly by 3?
20. 20.What is the smallest number you must add to 668 so that it divides exactly by 9?
21. 21.What is the smallest number you must take away from 980 so that it divides exactly by 11?
22. 22.How many factors does 82 have?
23. 23.What is the smallest number you must add to 786 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 418 so that it divides exactly by 12?
25. 25.How many factors does 86 have?
26. 26.What is the smallest number you must take away from 293 so that it divides exactly by 6?
27. 27.Which of these numbers divides exactly by 11? (a) 7941 (b) 8611 (c) 9999 (d) 1910
28. 28.What is the smallest number you must take away from 256 so that it divides exactly by 12?
29. 29.Which of these numbers divides exactly by 11? (a) 4461 (b) 2072 (c) 4307 (d) 5731
30. 30.What is the smallest number you must add to 995 so that it divides exactly by 11?
31. 31.What is the smallest number you must take away from 914 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 4? (a) 8000 (b) 5249 (c) 9385 (d) 8159
33. 33.Which of these numbers divides exactly by 9? (a) 6919 (b) 7965 (c) 2002 (d) 2785
34. 34.How many factors does 16 have?
35. 35.What is the smallest number you must add to 554 so that it divides exactly by 8?
36. 36.How many factors does 99 have?
37. 37.Which of these numbers divides exactly by 3? (a) 2012 (b) 7744 (c) 2574 (d) 4786
38. 38.What is the smallest number you must take away from 746 so that it divides exactly by 11?
39. 39.How many factors does 36 have?
40. 40.What is the smallest number you must take away from 284 so that it divides exactly by 3?

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