Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 30 · 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 64 have?
2. 2.What is the smallest number you must take away from 830 so that it divides exactly by 6?
3. 3.What is the smallest number you must add to 915 so that it divides exactly by 12?
4. 4.What is the smallest number you must add to 881 so that it divides exactly by 4?
5. 5.What is the smallest number you must add to 199 so that it divides exactly by 8?
6. 6.What is the smallest number you must add to 375 so that it divides exactly by 6?
7. 7.What is the smallest number you must add to 409 so that it divides exactly by 11?
8. 8.How many factors does 25 have?
9. 9.How many factors does 35 have?
10. 10.What is the smallest number you must take away from 477 so that it divides exactly by 13?
11. 11.Which of these numbers divides exactly by 11? (a) 3705 (b) 5212 (c) 2827 (d) 4074
12. 12.What is the smallest number you must add to 966 so that it divides exactly by 13?
13. 13.What is the smallest number you must add to 976 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 390 so that it divides exactly by 9?
15. 15.How many factors does 100 have?
16. 16.Which of these numbers divides exactly by 11? (a) 6040 (b) 7898 (c) 2832 (d) 7831
17. 17.What is the smallest number you must take away from 222 so that it divides exactly by 12?
18. 18.How many factors does 62 have?
19. 19.How many factors does 38 have?
20. 20.What is the smallest number you must take away from 950 so that it divides exactly by 3?
21. 21.How many factors does 31 have?
22. 22.How many factors does 70 have?
23. 23.Which of these numbers divides exactly by 8? (a) 4478 (b) 1376 (c) 1633 (d) 8845
24. 24.How many factors does 20 have?
25. 25.What is the smallest number you must add to 584 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 570 so that it divides exactly by 9?
27. 27.How many factors does 48 have?
28. 28.What is the smallest number you must take away from 278 so that it divides exactly by 4?
29. 29.What is the smallest number you must add to 259 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 819 so that it divides exactly by 4?
31. 31.Which of these numbers divides exactly by 8? (a) 3066 (b) 2760 (c) 9278 (d) 4017
32. 32.What is the smallest number you must add to 964 so that it divides exactly by 6?
33. 33.What is the smallest number you must take away from 663 so that it divides exactly by 8?
34. 34.What is the smallest number you must add to 748 so that it divides exactly by 6?
35. 35.Which of these numbers divides exactly by 3? (a) 4643 (b) 2645 (c) 9439 (d) 4698
36. 36.What is the smallest number you must add to 382 so that it divides exactly by 12?
37. 37.Which of these numbers divides exactly by 3? (a) 6173 (b) 8576 (c) 7712 (d) 4503
38. 38.What is the smallest number you must take away from 265 so that it divides exactly by 13?
39. 39.What is the smallest number you must add to 743 so that it divides exactly by 8?
40. 40.What is the smallest number you must add to 376 so that it divides exactly by 6?

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