Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 20 · 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.Which of these numbers divides exactly by 6? (a) 9596 (b) 3132 (c) 7879 (d) 8896
2. 2.What is the smallest number you must add to 930 so that it divides exactly by 7?
3. 3.How many factors does 31 have?
4. 4.Which of these numbers divides exactly by 8? (a) 3178 (b) 1406 (c) 4475 (d) 4240
5. 5.What is the smallest number you must add to 340 so that it divides exactly by 7?
6. 6.What is the smallest number you must take away from 546 so that it divides exactly by 9?
7. 7.What is the smallest number you must take away from 359 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 513 so that it divides exactly by 4?
9. 9.What is the smallest number you must take away from 903 so that it divides exactly by 13?
10. 10.How many factors does 13 have?
11. 11.How many factors does 20 have?
12. 12.What is the smallest number you must add to 233 so that it divides exactly by 9?
13. 13.How many factors does 28 have?
14. 14.Which of these numbers divides exactly by 3? (a) 9505 (b) 6685 (c) 5729 (d) 5409
15. 15.What is the smallest number you must add to 759 so that it divides exactly by 8?
16. 16.How many factors does 25 have?
17. 17.What is the smallest number you must add to 944 so that it divides exactly by 11?
18. 18.Which of these numbers divides exactly by 11? (a) 2882 (b) 9662 (c) 3309 (d) 7081
19. 19.How many factors does 93 have?
20. 20.How many factors does 44 have?
21. 21.What is the smallest number you must add to 634 so that it divides exactly by 13?
22. 22.How many factors does 24 have?
23. 23.What is the smallest number you must add to 259 so that it divides exactly by 4?
24. 24.What is the smallest number you must take away from 185 so that it divides exactly by 11?
25. 25.How many factors does 76 have?
26. 26.Which of these numbers divides exactly by 9? (a) 5547 (b) 8858 (c) 8694 (d) 3059
27. 27.Which of these numbers divides exactly by 4? (a) 6173 (b) 8790 (c) 9192 (d) 2774
28. 28.Which of these numbers divides exactly by 8? (a) 9290 (b) 3146 (c) 3138 (d) 9208
29. 29.What is the smallest number you must take away from 914 so that it divides exactly by 6?
30. 30.How many factors does 51 have?
31. 31.Which of these numbers divides exactly by 9? (a) 5368 (b) 1458 (c) 1903 (d) 4462
32. 32.How many factors does 56 have?
33. 33.Which of these numbers divides exactly by 11? (a) 3345 (b) 1461 (c) 6721 (d) 5381
34. 34.What is the smallest number you must take away from 597 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 702 so that it divides exactly by 4?
36. 36.How many factors does 78 have?
37. 37.Which of these numbers divides exactly by 8? (a) 2958 (b) 1480 (c) 2683 (d) 9797
38. 38.What is the smallest number you must take away from 107 so that it divides exactly by 12?
39. 39.Which of these numbers divides exactly by 4? (a) 2934 (b) 8656 (c) 4191 (d) 1078
40. 40.Which of these numbers divides exactly by 9? (a) 8294 (b) 2415 (c) 6426 (d) 7773

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