Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 290 · 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 70 have?
2. 2.What is the smallest number you must add to 137 so that it divides exactly by 4?
3. 3.Which of these numbers divides exactly by 11? (a) 2400 (b) 6229 (c) 5728 (d) 3916
4. 4.How many factors does 60 have?
5. 5.How many factors does 39 have?
6. 6.What is the smallest number you must add to 847 so that it divides exactly by 3?
7. 7.What is the smallest number you must take away from 533 so that it divides exactly by 7?
8. 8.What is the smallest number you must add to 596 so that it divides exactly by 6?
9. 9.What is the smallest number you must take away from 508 so that it divides exactly by 9?
10. 10.How many factors does 22 have?
11. 11.Which of these numbers divides exactly by 6? (a) 5594 (b) 1902 (c) 1010 (d) 2331
12. 12.What is the smallest number you must take away from 499 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 724 so that it divides exactly by 6?
14. 14.What is the smallest number you must add to 955 so that it divides exactly by 7?
15. 15.What is the smallest number you must take away from 595 so that it divides exactly by 6?
16. 16.Which of these numbers divides exactly by 4? (a) 7891 (b) 7126 (c) 9312 (d) 2069
17. 17.What is the smallest number you must add to 251 so that it divides exactly by 12?
18. 18.How many factors does 92 have?
19. 19.What is the smallest number you must take away from 587 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 107 so that it divides exactly by 12?
21. 21.Which of these numbers divides exactly by 11? (a) 1630 (b) 3586 (c) 5023 (d) 1350
22. 22.What is the smallest number you must add to 227 so that it divides exactly by 6?
23. 23.Which of these numbers divides exactly by 3? (a) 5927 (b) 2987 (c) 4249 (d) 7890
24. 24.How many factors does 77 have?
25. 25.What is the smallest number you must add to 301 so that it divides exactly by 9?
26. 26.What is the smallest number you must add to 472 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 933 so that it divides exactly by 13?
28. 28.What is the smallest number you must take away from 253 so that it divides exactly by 8?
29. 29.Which of these numbers divides exactly by 4? (a) 7617 (b) 3068 (c) 8879 (d) 3915
30. 30.What is the smallest number you must add to 770 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 4? (a) 7729 (b) 7269 (c) 1804 (d) 3954
32. 32.How many factors does 90 have?
33. 33.What is the smallest number you must take away from 233 so that it divides exactly by 8?
34. 34.What is the smallest number you must add to 307 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 3? (a) 2618 (b) 1882 (c) 8224 (d) 9096
36. 36.What is the smallest number you must add to 545 so that it divides exactly by 7?
37. 37.How many factors does 94 have?
38. 38.Which of these numbers divides exactly by 6? (a) 2122 (b) 6804 (c) 4233 (d) 7631
39. 39.How many factors does 37 have?
40. 40.What is the smallest number you must add to 427 so that it divides exactly by 4?

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