Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 212 · 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.How many factors does 27 have?
2. 2.How many factors does 38 have?
3. 3.What is the smallest number you must take away from 816 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 3? (a) 7270 (b) 8477 (c) 4907 (d) 5079
5. 5.What is the smallest number you must take away from 160 so that it divides exactly by 3?
6. 6.What is the smallest number you must add to 350 so that it divides exactly by 11?
7. 7.Which of these numbers divides exactly by 11? (a) 3017 (b) 8570 (c) 4669 (d) 4378
8. 8.How many factors does 21 have?
9. 9.Which of these numbers divides exactly by 9? (a) 1997 (b) 9751 (c) 4518 (d) 6008
10. 10.How many factors does 76 have?
11. 11.What is the smallest number you must take away from 281 so that it divides exactly by 6?
12. 12.What is the smallest number you must take away from 625 so that it divides exactly by 6?
13. 13.Which of these numbers divides exactly by 4? (a) 5856 (b) 2558 (c) 7255 (d) 5859
14. 14.What is the smallest number you must take away from 412 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 295 so that it divides exactly by 7?
16. 16.What is the smallest number you must take away from 874 so that it divides exactly by 8?
17. 17.What is the smallest number you must take away from 958 so that it divides exactly by 7?
18. 18.Which of these numbers divides exactly by 4? (a) 5197 (b) 8040 (c) 4506 (d) 2509
19. 19.Which of these numbers divides exactly by 4? (a) 6961 (b) 1645 (c) 9044 (d) 5283
20. 20.What is the smallest number you must add to 618 so that it divides exactly by 7?
21. 21.Which of these numbers divides exactly by 6? (a) 7986 (b) 1363 (c) 9919 (d) 6907
22. 22.What is the smallest number you must add to 589 so that it divides exactly by 6?
23. 23.What is the smallest number you must add to 334 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 883 so that it divides exactly by 9?
25. 25.How many factors does 46 have?
26. 26.Which of these numbers divides exactly by 3? (a) 2840 (b) 5400 (c) 7667 (d) 8371
27. 27.What is the smallest number you must add to 318 so that it divides exactly by 11?
28. 28.How many factors does 67 have?
29. 29.What is the smallest number you must take away from 395 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 3? (a) 9268 (b) 1599 (c) 4040 (d) 2017
31. 31.What is the smallest number you must take away from 537 so that it divides exactly by 12?
32. 32.What is the smallest number you must take away from 573 so that it divides exactly by 8?
33. 33.Which of these numbers divides exactly by 3? (a) 3238 (b) 8844 (c) 4910 (d) 4654
34. 34.Which of these numbers divides exactly by 8? (a) 2571 (b) 4992 (c) 5020 (d) 8125
35. 35.What is the smallest number you must add to 781 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 4? (a) 2306 (b) 6836 (c) 5489 (d) 2747
37. 37.What is the smallest number you must take away from 158 so that it divides exactly by 8?
38. 38.How many factors does 97 have?
39. 39.What is the smallest number you must take away from 780 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 332 so that it divides exactly by 3?

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