Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 283 · 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 add to 647 so that it divides exactly by 8?
2. 2.What is the smallest number you must take away from 719 so that it divides exactly by 3?
3. 3.Which of these numbers divides exactly by 6? (a) 6215 (b) 9946 (c) 9316 (d) 3156
4. 4.How many factors does 59 have?
5. 5.Which of these numbers divides exactly by 8? (a) 8439 (b) 8008 (c) 8721 (d) 2773
6. 6.How many factors does 33 have?
7. 7.What is the smallest number you must add to 277 so that it divides exactly by 8?
8. 8.What is the smallest number you must take away from 527 so that it divides exactly by 4?
9. 9.What is the smallest number you must take away from 886 so that it divides exactly by 3?
10. 10.Which of these numbers divides exactly by 6? (a) 7527 (b) 9141 (c) 5126 (d) 6720
11. 11.Which of these numbers divides exactly by 8? (a) 7520 (b) 8623 (c) 1396 (d) 2681
12. 12.Which of these numbers divides exactly by 11? (a) 3236 (b) 7366 (c) 9038 (d) 5643
13. 13.How many factors does 39 have?
14. 14.How many factors does 71 have?
15. 15.What is the smallest number you must take away from 955 so that it divides exactly by 3?
16. 16.How many factors does 15 have?
17. 17.What is the smallest number you must add to 888 so that it divides exactly by 11?
18. 18.What is the smallest number you must take away from 437 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 554 so that it divides exactly by 11?
20. 20.Which of these numbers divides exactly by 4? (a) 5817 (b) 8449 (c) 5717 (d) 1372
21. 21.What is the smallest number you must take away from 442 so that it divides exactly by 9?
22. 22.How many factors does 26 have?
23. 23.How many factors does 24 have?
24. 24.What is the smallest number you must take away from 146 so that it divides exactly by 7?
25. 25.Which of these numbers divides exactly by 6? (a) 8734 (b) 5218 (c) 4452 (d) 4299
26. 26.Which of these numbers divides exactly by 3? (a) 9520 (b) 8022 (c) 4892 (d) 2884
27. 27.Which of these numbers divides exactly by 8? (a) 5749 (b) 3221 (c) 7008 (d) 5471
28. 28.What is the smallest number you must take away from 447 so that it divides exactly by 6?
29. 29.What is the smallest number you must add to 103 so that it divides exactly by 13?
30. 30.How many factors does 87 have?
31. 31.What is the smallest number you must take away from 290 so that it divides exactly by 4?
32. 32.What is the smallest number you must take away from 697 so that it divides exactly by 11?
33. 33.Which of these numbers divides exactly by 9? (a) 9989 (b) 9346 (c) 2529 (d) 7012
34. 34.What is the smallest number you must take away from 340 so that it divides exactly by 8?
35. 35.What is the smallest number you must take away from 417 so that it divides exactly by 9?
36. 36.How many factors does 86 have?
37. 37.What is the smallest number you must add to 335 so that it divides exactly by 11?
38. 38.Which of these numbers divides exactly by 9? (a) 1822 (b) 2916 (c) 9184 (d) 9583
39. 39.What is the smallest number you must add to 101 so that it divides exactly by 3?
40. 40.What is the smallest number you must add to 108 so that it divides exactly by 13?

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