Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 233 · 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 935 so that it divides exactly by 8?
2. 2.Which of these numbers divides exactly by 11? (a) 1931 (b) 6985 (c) 6538 (d) 1921
3. 3.What is the smallest number you must add to 857 so that it divides exactly by 9?
4. 4.What is the smallest number you must add to 351 so that it divides exactly by 6?
5. 5.Which of these numbers divides exactly by 6? (a) 1524 (b) 7523 (c) 3886 (d) 4987
6. 6.What is the smallest number you must add to 925 so that it divides exactly by 7?
7. 7.Which of these numbers divides exactly by 8? (a) 3784 (b) 8482 (c) 3454 (d) 9110
8. 8.Which of these numbers divides exactly by 6? (a) 3380 (b) 1447 (c) 4638 (d) 1610
9. 9.How many factors does 30 have?
10. 10.How many factors does 27 have?
11. 11.What is the smallest number you must take away from 269 so that it divides exactly by 9?
12. 12.How many factors does 63 have?
13. 13.What is the smallest number you must add to 493 so that it divides exactly by 3?
14. 14.Which of these numbers divides exactly by 4? (a) 3735 (b) 3034 (c) 9822 (d) 7652
15. 15.Which of these numbers divides exactly by 4? (a) 1784 (b) 7477 (c) 8199 (d) 8674
16. 16.Which of these numbers divides exactly by 6? (a) 1749 (b) 7356 (c) 9563 (d) 3585
17. 17.What is the smallest number you must add to 950 so that it divides exactly by 3?
18. 18.How many factors does 75 have?
19. 19.Which of these numbers divides exactly by 3? (a) 8607 (b) 4870 (c) 2180 (d) 6967
20. 20.What is the smallest number you must take away from 329 so that it divides exactly by 12?
21. 21.What is the smallest number you must take away from 438 so that it divides exactly by 9?
22. 22.How many factors does 29 have?
23. 23.How many factors does 84 have?
24. 24.Which of these numbers divides exactly by 11? (a) 9037 (b) 4099 (c) 5272 (d) 4499
25. 25.What is the smallest number you must add to 395 so that it divides exactly by 7?
26. 26.What is the smallest number you must take away from 135 so that it divides exactly by 13?
27. 27.What is the smallest number you must take away from 662 so that it divides exactly by 7?
28. 28.Which of these numbers divides exactly by 4? (a) 1060 (b) 5711 (c) 7667 (d) 9609
29. 29.Which of these numbers divides exactly by 11? (a) 6006 (b) 4265 (c) 7409 (d) 1777
30. 30.What is the smallest number you must add to 808 so that it divides exactly by 13?
31. 31.What is the smallest number you must add to 218 so that it divides exactly by 3?
32. 32.Which of these numbers divides exactly by 11? (a) 4964 (b) 9977 (c) 7778 (d) 8258
33. 33.What is the smallest number you must take away from 378 so that it divides exactly by 4?
34. 34.What is the smallest number you must add to 605 so that it divides exactly by 8?
35. 35.How many factors does 51 have?
36. 36.Which of these numbers divides exactly by 3? (a) 3440 (b) 7872 (c) 2983 (d) 4373
37. 37.Which of these numbers divides exactly by 3? (a) 4762 (b) 1130 (c) 9902 (d) 8955
38. 38.What is the smallest number you must add to 743 so that it divides exactly by 7?
39. 39.Which of these numbers divides exactly by 3? (a) 1016 (b) 8705 (c) 2417 (d) 8217
40. 40.What is the smallest number you must add to 433 so that it divides exactly by 8?

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