Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 277 · 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) 6604 (b) 2660 (c) 1336 (d) 8685
2. 2.What is the smallest number you must take away from 796 so that it divides exactly by 11?
3. 3.How many factors does 17 have?
4. 4.What is the smallest number you must take away from 301 so that it divides exactly by 12?
5. 5.Which of these numbers divides exactly by 9? (a) 5563 (b) 1322 (c) 5919 (d) 7749
6. 6.Which of these numbers divides exactly by 11? (a) 2296 (b) 4780 (c) 6359 (d) 8030
7. 7.What is the smallest number you must add to 415 so that it divides exactly by 6?
8. 8.How many factors does 73 have?
9. 9.How many factors does 81 have?
10. 10.Which of these numbers divides exactly by 6? (a) 5770 (b) 8620 (c) 2748 (d) 2271
11. 11.Which of these numbers divides exactly by 4? (a) 3276 (b) 5182 (c) 6562 (d) 6597
12. 12.What is the smallest number you must add to 664 so that it divides exactly by 6?
13. 13.What is the smallest number you must take away from 369 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 637 so that it divides exactly by 12?
15. 15.What is the smallest number you must add to 270 so that it divides exactly by 4?
16. 16.What is the smallest number you must add to 377 so that it divides exactly by 9?
17. 17.How many factors does 36 have?
18. 18.What is the smallest number you must take away from 138 so that it divides exactly by 9?
19. 19.What is the smallest number you must take away from 113 so that it divides exactly by 6?
20. 20.How many factors does 48 have?
21. 21.How many factors does 53 have?
22. 22.What is the smallest number you must add to 192 so that it divides exactly by 7?
23. 23.How many factors does 69 have?
24. 24.Which of these numbers divides exactly by 6? (a) 5382 (b) 1600 (c) 4210 (d) 1899
25. 25.What is the smallest number you must take away from 690 so that it divides exactly by 8?
26. 26.What is the smallest number you must take away from 281 so that it divides exactly by 3?
27. 27.What is the smallest number you must add to 228 so that it divides exactly by 7?
28. 28.Which of these numbers divides exactly by 6? (a) 3609 (b) 2044 (c) 6550 (d) 2286
29. 29.Which of these numbers divides exactly by 4? (a) 6810 (b) 4132 (c) 3838 (d) 7003
30. 30.Which of these numbers divides exactly by 9? (a) 3749 (b) 1332 (c) 8058 (d) 9839
31. 31.What is the smallest number you must take away from 221 so that it divides exactly by 11?
32. 32.What is the smallest number you must take away from 752 so that it divides exactly by 7?
33. 33.How many factors does 24 have?
34. 34.What is the smallest number you must add to 635 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 11? (a) 3129 (b) 6644 (c) 4039 (d) 3120
36. 36.What is the smallest number you must take away from 413 so that it divides exactly by 3?
37. 37.How many factors does 20 have?
38. 38.What is the smallest number you must add to 463 so that it divides exactly by 11?
39. 39.What is the smallest number you must add to 992 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 874 so that it divides exactly by 8?

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