Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 275 · 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 408 so that it divides exactly by 9?
2. 2.What is the smallest number you must add to 646 so that it divides exactly by 3?
3. 3.What is the smallest number you must take away from 649 so that it divides exactly by 12?
4. 4.What is the smallest number you must take away from 566 so that it divides exactly by 6?
5. 5.How many factors does 14 have?
6. 6.How many factors does 77 have?
7. 7.What is the smallest number you must add to 631 so that it divides exactly by 4?
8. 8.What is the smallest number you must take away from 682 so that it divides exactly by 3?
9. 9.What is the smallest number you must take away from 525 so that it divides exactly by 6?
10. 10.What is the smallest number you must add to 949 so that it divides exactly by 7?
11. 11.Which of these numbers divides exactly by 6? (a) 2872 (b) 5621 (c) 1770 (d) 5528
12. 12.What is the smallest number you must take away from 902 so that it divides exactly by 12?
13. 13.Which of these numbers divides exactly by 6? (a) 5927 (b) 7010 (c) 3802 (d) 3396
14. 14.How many factors does 79 have?
15. 15.How many factors does 90 have?
16. 16.What is the smallest number you must take away from 213 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 3? (a) 2199 (b) 9925 (c) 5675 (d) 6319
18. 18.Which of these numbers divides exactly by 9? (a) 3545 (b) 8176 (c) 6147 (d) 9655
19. 19.What is the smallest number you must take away from 474 so that it divides exactly by 4?
20. 20.What is the smallest number you must take away from 584 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 256 so that it divides exactly by 7?
22. 22.What is the smallest number you must take away from 463 so that it divides exactly by 9?
23. 23.What is the smallest number you must add to 237 so that it divides exactly by 11?
24. 24.What is the smallest number you must take away from 293 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 332 so that it divides exactly by 6?
26. 26.How many factors does 91 have?
27. 27.How many factors does 88 have?
28. 28.How many factors does 25 have?
29. 29.What is the smallest number you must take away from 907 so that it divides exactly by 6?
30. 30.How many factors does 66 have?
31. 31.What is the smallest number you must add to 873 so that it divides exactly by 12?
32. 32.How many factors does 84 have?
33. 33.What is the smallest number you must add to 853 so that it divides exactly by 6?
34. 34.What is the smallest number you must take away from 786 so that it divides exactly by 13?
35. 35.How many factors does 73 have?
36. 36.How many factors does 61 have?
37. 37.Which of these numbers divides exactly by 4? (a) 8852 (b) 8945 (c) 1689 (d) 5165
38. 38.What is the smallest number you must add to 276 so that it divides exactly by 9?
39. 39.What is the smallest number you must add to 396 so that it divides exactly by 7?
40. 40.How many factors does 26 have?

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