Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 44 · 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 3? (a) 7875 (b) 8950 (c) 2083 (d) 6985
2. 2.How many factors does 48 have?
3. 3.How many factors does 87 have?
4. 4.How many factors does 49 have?
5. 5.Which of these numbers divides exactly by 8? (a) 8693 (b) 2300 (c) 7616 (d) 8133
6. 6.What is the smallest number you must take away from 436 so that it divides exactly by 6?
7. 7.What is the smallest number you must add to 677 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 192 so that it divides exactly by 9?
9. 9.What is the smallest number you must take away from 914 so that it divides exactly by 4?
10. 10.How many factors does 15 have?
11. 11.What is the smallest number you must add to 434 so that it divides exactly by 6?
12. 12.How many factors does 19 have?
13. 13.Which of these numbers divides exactly by 3? (a) 8311 (b) 5733 (c) 5003 (d) 5752
14. 14.Which of these numbers divides exactly by 6? (a) 4849 (b) 1752 (c) 2321 (d) 7481
15. 15.Which of these numbers divides exactly by 8? (a) 4740 (b) 3416 (c) 2402 (d) 7972
16. 16.Which of these numbers divides exactly by 3? (a) 8825 (b) 5560 (c) 4817 (d) 6105
17. 17.How many factors does 85 have?
18. 18.Which of these numbers divides exactly by 6? (a) 9288 (b) 1939 (c) 2636 (d) 1589
19. 19.What is the smallest number you must add to 113 so that it divides exactly by 7?
20. 20.How many factors does 32 have?
21. 21.What is the smallest number you must take away from 304 so that it divides exactly by 11?
22. 22.What is the smallest number you must take away from 846 so that it divides exactly by 4?
23. 23.What is the smallest number you must take away from 434 so that it divides exactly by 11?
24. 24.What is the smallest number you must add to 113 so that it divides exactly by 13?
25. 25.Which of these numbers divides exactly by 4? (a) 7809 (b) 6551 (c) 4862 (d) 4220
26. 26.How many factors does 82 have?
27. 27.How many factors does 73 have?
28. 28.Which of these numbers divides exactly by 11? (a) 1954 (b) 2915 (c) 4786 (d) 9576
29. 29.What is the smallest number you must take away from 385 so that it divides exactly by 9?
30. 30.Which of these numbers divides exactly by 4? (a) 6697 (b) 9083 (c) 1087 (d) 1396
31. 31.Which of these numbers divides exactly by 11? (a) 5280 (b) 4864 (c) 6544 (d) 1406
32. 32.What is the smallest number you must add to 627 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 6? (a) 2235 (b) 1741 (c) 3740 (d) 9678
34. 34.Which of these numbers divides exactly by 9? (a) 1432 (b) 7538 (c) 2479 (d) 5157
35. 35.What is the smallest number you must add to 847 so that it divides exactly by 3?
36. 36.What is the smallest number you must add to 355 so that it divides exactly by 8?
37. 37.How many factors does 60 have?
38. 38.Which of these numbers divides exactly by 11? (a) 4372 (b) 3173 (c) 8104 (d) 6743
39. 39.What is the smallest number you must add to 308 so that it divides exactly by 8?
40. 40.What is the smallest number you must take away from 277 so that it divides exactly by 8?

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