Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 167 · 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.What is the smallest number you must add to 203 so that it divides exactly by 8?
2. 2.What is the smallest number you must add to 836 so that it divides exactly by 3?
3. 3.Which of these numbers divides exactly by 8? (a) 3971 (b) 4148 (c) 9068 (d) 6816
4. 4.What is the smallest number you must take away from 492 so that it divides exactly by 13?
5. 5.Which of these numbers divides exactly by 11? (a) 9097 (b) 8532 (c) 4904 (d) 5836
6. 6.What is the smallest number you must add to 718 so that it divides exactly by 3?
7. 7.How many factors does 28 have?
8. 8.Which of these numbers divides exactly by 4? (a) 2939 (b) 5061 (c) 2200 (d) 2454
9. 9.What is the smallest number you must take away from 232 so that it divides exactly by 7?
10. 10.What is the smallest number you must take away from 899 so that it divides exactly by 8?
11. 11.How many factors does 16 have?
12. 12.How many factors does 57 have?
13. 13.What is the smallest number you must take away from 953 so that it divides exactly by 8?
14. 14.What is the smallest number you must add to 591 so that it divides exactly by 11?
15. 15.How many factors does 39 have?
16. 16.Which of these numbers divides exactly by 11? (a) 4420 (b) 1150 (c) 4827 (d) 5203
17. 17.How many factors does 17 have?
18. 18.What is the smallest number you must take away from 910 so that it divides exactly by 12?
19. 19.What is the smallest number you must add to 663 so that it divides exactly by 12?
20. 20.What is the smallest number you must add to 130 so that it divides exactly by 8?
21. 21.How many factors does 84 have?
22. 22.How many factors does 30 have?
23. 23.How many factors does 63 have?
24. 24.What is the smallest number you must take away from 230 so that it divides exactly by 4?
25. 25.How many factors does 35 have?
26. 26.What is the smallest number you must add to 938 so that it divides exactly by 9?
27. 27.Which of these numbers divides exactly by 11? (a) 2689 (b) 1874 (c) 8459 (d) 9128
28. 28.Which of these numbers divides exactly by 8? (a) 9736 (b) 1836 (c) 7945 (d) 1681
29. 29.What is the smallest number you must take away from 361 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 166 so that it divides exactly by 4?
31. 31.What is the smallest number you must take away from 788 so that it divides exactly by 12?
32. 32.What is the smallest number you must add to 308 so that it divides exactly by 9?
33. 33.What is the smallest number you must take away from 568 so that it divides exactly by 9?
34. 34.What is the smallest number you must take away from 637 so that it divides exactly by 12?
35. 35.How many factors does 98 have?
36. 36.What is the smallest number you must add to 202 so that it divides exactly by 13?
37. 37.What is the smallest number you must take away from 619 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 769 so that it divides exactly by 3?
39. 39.How many factors does 62 have?
40. 40.Which of these numbers divides exactly by 3? (a) 1681 (b) 5241 (c) 5953 (d) 4358

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