Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 86 · 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 933 so that it divides exactly by 12?
2. 2.How many factors does 95 have?
3. 3.How many factors does 65 have?
4. 4.Which of these numbers divides exactly by 6? (a) 2267 (b) 6272 (c) 6806 (d) 9048
5. 5.What is the smallest number you must take away from 291 so that it divides exactly by 7?
6. 6.What is the smallest number you must add to 497 so that it divides exactly by 4?
7. 7.Which of these numbers divides exactly by 4? (a) 1956 (b) 2863 (c) 5466 (d) 8055
8. 8.Which of these numbers divides exactly by 9? (a) 7317 (b) 6186 (c) 4832 (d) 2065
9. 9.How many factors does 49 have?
10. 10.Which of these numbers divides exactly by 3? (a) 7627 (b) 8602 (c) 3762 (d) 4085
11. 11.What is the smallest number you must add to 926 so that it divides exactly by 9?
12. 12.What is the smallest number you must add to 593 so that it divides exactly by 11?
13. 13.Which of these numbers divides exactly by 4? (a) 4780 (b) 2919 (c) 2630 (d) 9462
14. 14.What is the smallest number you must take away from 913 so that it divides exactly by 7?
15. 15.What is the smallest number you must add to 649 so that it divides exactly by 6?
16. 16.What is the smallest number you must take away from 183 so that it divides exactly by 11?
17. 17.What is the smallest number you must add to 817 so that it divides exactly by 12?
18. 18.Which of these numbers divides exactly by 4? (a) 9449 (b) 4468 (c) 8299 (d) 3723
19. 19.Which of these numbers divides exactly by 6? (a) 7350 (b) 2479 (c) 8824 (d) 2248
20. 20.What is the smallest number you must add to 178 so that it divides exactly by 4?
21. 21.How many factors does 61 have?
22. 22.What is the smallest number you must add to 273 so that it divides exactly by 12?
23. 23.What is the smallest number you must add to 843 so that it divides exactly by 12?
24. 24.Which of these numbers divides exactly by 9? (a) 2544 (b) 5659 (c) 1305 (d) 9362
25. 25.What is the smallest number you must take away from 187 so that it divides exactly by 6?
26. 26.Which of these numbers divides exactly by 4? (a) 5774 (b) 3453 (c) 8960 (d) 7815
27. 27.Which of these numbers divides exactly by 6? (a) 4426 (b) 9861 (c) 1842 (d) 7454
28. 28.How many factors does 72 have?
29. 29.What is the smallest number you must add to 493 so that it divides exactly by 4?
30. 30.How many factors does 28 have?
31. 31.How many factors does 24 have?
32. 32.What is the smallest number you must add to 998 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 673 so that it divides exactly by 12?
34. 34.How many factors does 18 have?
35. 35.How many factors does 79 have?
36. 36.What is the smallest number you must add to 219 so that it divides exactly by 8?
37. 37.How many factors does 14 have?
38. 38.How many factors does 32 have?
39. 39.Which of these numbers divides exactly by 11? (a) 7836 (b) 2423 (c) 7370 (d) 4534
40. 40.How many factors does 25 have?

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