Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 39 · 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 100 have?
2. 2.What is the smallest number you must take away from 177 so that it divides exactly by 4?
3. 3.What is the smallest number you must take away from 212 so that it divides exactly by 11?
4. 4.What is the smallest number you must add to 244 so that it divides exactly by 3?
5. 5.What is the smallest number you must take away from 691 so that it divides exactly by 13?
6. 6.What is the smallest number you must add to 980 so that it divides exactly by 3?
7. 7.What is the smallest number you must add to 404 so that it divides exactly by 11?
8. 8.How many factors does 99 have?
9. 9.What is the smallest number you must take away from 769 so that it divides exactly by 6?
10. 10.How many factors does 41 have?
11. 11.What is the smallest number you must take away from 163 so that it divides exactly by 3?
12. 12.How many factors does 72 have?
13. 13.How many factors does 74 have?
14. 14.Which of these numbers divides exactly by 11? (a) 1327 (b) 6708 (c) 3702 (d) 2904
15. 15.What is the smallest number you must take away from 484 so that it divides exactly by 8?
16. 16.What is the smallest number you must take away from 821 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 3? (a) 5922 (b) 5302 (c) 6755 (d) 9007
18. 18.Which of these numbers divides exactly by 6? (a) 3117 (b) 9036 (c) 5926 (d) 7517
19. 19.How many factors does 86 have?
20. 20.What is the smallest number you must add to 179 so that it divides exactly by 4?
21. 21.What is the smallest number you must add to 742 so that it divides exactly by 8?
22. 22.Which of these numbers divides exactly by 9? (a) 5584 (b) 2610 (c) 8111 (d) 6334
23. 23.Which of these numbers divides exactly by 8? (a) 2835 (b) 4926 (c) 1748 (d) 3064
24. 24.What is the smallest number you must take away from 135 so that it divides exactly by 4?
25. 25.What is the smallest number you must add to 902 so that it divides exactly by 3?
26. 26.How many factors does 71 have?
27. 27.How many factors does 29 have?
28. 28.What is the smallest number you must take away from 954 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 548 so that it divides exactly by 7?
30. 30.What is the smallest number you must take away from 686 so that it divides exactly by 9?
31. 31.Which of these numbers divides exactly by 3? (a) 1292 (b) 1654 (c) 8017 (d) 8244
32. 32.What is the smallest number you must add to 956 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 6? (a) 6722 (b) 9574 (c) 5683 (d) 3108
34. 34.How many factors does 23 have?
35. 35.What is the smallest number you must take away from 413 so that it divides exactly by 12?
36. 36.What is the smallest number you must add to 248 so that it divides exactly by 12?
37. 37.How many factors does 75 have?
38. 38.What is the smallest number you must add to 850 so that it divides exactly by 7?
39. 39.What is the smallest number you must take away from 937 so that it divides exactly by 4?
40. 40.How many factors does 39 have?

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