Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 251 · 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 take away from 635 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 502 so that it divides exactly by 7?
3. 3.What is the smallest number you must add to 625 so that it divides exactly by 3?
4. 4.What is the smallest number you must take away from 668 so that it divides exactly by 7?
5. 5.What is the smallest number you must add to 139 so that it divides exactly by 8?
6. 6.What is the smallest number you must take away from 380 so that it divides exactly by 9?
7. 7.What is the smallest number you must take away from 171 so that it divides exactly by 7?
8. 8.How many factors does 31 have?
9. 9.How many factors does 42 have?
10. 10.What is the smallest number you must take away from 741 so that it divides exactly by 7?
11. 11.What is the smallest number you must take away from 506 so that it divides exactly by 8?
12. 12.What is the smallest number you must take away from 797 so that it divides exactly by 9?
13. 13.What is the smallest number you must take away from 471 so that it divides exactly by 12?
14. 14.Which of these numbers divides exactly by 9? (a) 7056 (b) 7719 (c) 1402 (d) 4200
15. 15.Which of these numbers divides exactly by 3? (a) 3847 (b) 4480 (c) 1953 (d) 6178
16. 16.Which of these numbers divides exactly by 4? (a) 2218 (b) 3897 (c) 1602 (d) 8836
17. 17.What is the smallest number you must take away from 809 so that it divides exactly by 6?
18. 18.What is the smallest number you must take away from 275 so that it divides exactly by 9?
19. 19.How many factors does 33 have?
20. 20.Which of these numbers divides exactly by 6? (a) 8469 (b) 1350 (c) 9850 (d) 8186
21. 21.Which of these numbers divides exactly by 6? (a) 1193 (b) 1549 (c) 1294 (d) 4944
22. 22.What is the smallest number you must take away from 390 so that it divides exactly by 9?
23. 23.What is the smallest number you must add to 529 so that it divides exactly by 13?
24. 24.How many factors does 99 have?
25. 25.Which of these numbers divides exactly by 8? (a) 3457 (b) 4276 (c) 1831 (d) 8944
26. 26.How many factors does 39 have?
27. 27.What is the smallest number you must add to 241 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 328 so that it divides exactly by 7?
29. 29.How many factors does 28 have?
30. 30.What is the smallest number you must take away from 801 so that it divides exactly by 7?
31. 31.How many factors does 35 have?
32. 32.What is the smallest number you must add to 898 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 103 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 817 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 11? (a) 4368 (b) 4081 (c) 6704 (d) 4794
36. 36.How many factors does 64 have?
37. 37.What is the smallest number you must take away from 607 so that it divides exactly by 9?
38. 38.Which of these numbers divides exactly by 11? (a) 3069 (b) 4823 (c) 5044 (d) 3184
39. 39.What is the smallest number you must add to 927 so that it divides exactly by 6?
40. 40.Which of these numbers divides exactly by 8? (a) 1611 (b) 8886 (c) 2304 (d) 8284

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