Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 21 · 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 34 have?
2. 2.What is the smallest number you must add to 361 so that it divides exactly by 12?
3. 3.How many factors does 66 have?
4. 4.What is the smallest number you must add to 788 so that it divides exactly by 13?
5. 5.What is the smallest number you must add to 239 so that it divides exactly by 11?
6. 6.Which of these numbers divides exactly by 9? (a) 5382 (b) 5489 (c) 6544 (d) 6909
7. 7.What is the smallest number you must add to 678 so that it divides exactly by 9?
8. 8.Which of these numbers divides exactly by 11? (a) 6535 (b) 9845 (c) 9566 (d) 1247
9. 9.Which of these numbers divides exactly by 4? (a) 6161 (b) 8747 (c) 6920 (d) 9287
10. 10.What is the smallest number you must take away from 453 so that it divides exactly by 11?
11. 11.Which of these numbers divides exactly by 6? (a) 8886 (b) 3371 (c) 2831 (d) 6447
12. 12.How many factors does 41 have?
13. 13.Which of these numbers divides exactly by 9? (a) 6057 (b) 2908 (c) 5295 (d) 9294
14. 14.How many factors does 72 have?
15. 15.What is the smallest number you must add to 734 so that it divides exactly by 3?
16. 16.What is the smallest number you must add to 897 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 8? (a) 7819 (b) 1288 (c) 4677 (d) 9959
18. 18.What is the smallest number you must add to 402 so that it divides exactly by 4?
19. 19.What is the smallest number you must add to 149 so that it divides exactly by 13?
20. 20.How many factors does 32 have?
21. 21.Which of these numbers divides exactly by 4? (a) 4086 (b) 8836 (c) 5037 (d) 3126
22. 22.Which of these numbers divides exactly by 8? (a) 8620 (b) 1467 (c) 8136 (d) 1693
23. 23.How many factors does 18 have?
24. 24.What is the smallest number you must take away from 605 so that it divides exactly by 3?
25. 25.How many factors does 47 have?
26. 26.What is the smallest number you must take away from 713 so that it divides exactly by 11?
27. 27.Which of these numbers divides exactly by 11? (a) 5973 (b) 6975 (c) 4981 (d) 6494
28. 28.How many factors does 59 have?
29. 29.How many factors does 77 have?
30. 30.Which of these numbers divides exactly by 6? (a) 3600 (b) 9813 (c) 9119 (d) 3944
31. 31.Which of these numbers divides exactly by 11? (a) 3953 (b) 3627 (c) 2382 (d) 1903
32. 32.How many factors does 97 have?
33. 33.Which of these numbers divides exactly by 3? (a) 2804 (b) 8264 (c) 7641 (d) 8054
34. 34.What is the smallest number you must add to 719 so that it divides exactly by 6?
35. 35.Which of these numbers divides exactly by 6? (a) 3461 (b) 6211 (c) 9834 (d) 4388
36. 36.How many factors does 19 have?
37. 37.Which of these numbers divides exactly by 4? (a) 2565 (b) 5342 (c) 2372 (d) 5714
38. 38.What is the smallest number you must add to 416 so that it divides exactly by 6?
39. 39.What is the smallest number you must take away from 563 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 368 so that it divides exactly by 13?

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