Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 116 · 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 68 have?
2. 2.What is the smallest number you must add to 677 so that it divides exactly by 11?
3. 3.What is the smallest number you must add to 697 so that it divides exactly by 9?
4. 4.What is the smallest number you must take away from 973 so that it divides exactly by 4?
5. 5.What is the smallest number you must take away from 373 so that it divides exactly by 3?
6. 6.What is the smallest number you must add to 135 so that it divides exactly by 11?
7. 7.What is the smallest number you must add to 469 so that it divides exactly by 4?
8. 8.How many factors does 32 have?
9. 9.What is the smallest number you must add to 476 so that it divides exactly by 11?
10. 10.How many factors does 57 have?
11. 11.Which of these numbers divides exactly by 11? (a) 4395 (b) 4567 (c) 5357 (d) 8336
12. 12.What is the smallest number you must take away from 355 so that it divides exactly by 8?
13. 13.Which of these numbers divides exactly by 3? (a) 4349 (b) 3156 (c) 9713 (d) 1579
14. 14.Which of these numbers divides exactly by 3? (a) 8913 (b) 4265 (c) 9533 (d) 3349
15. 15.Which of these numbers divides exactly by 11? (a) 6205 (b) 6364 (c) 1166 (d) 9115
16. 16.Which of these numbers divides exactly by 4? (a) 6163 (b) 1064 (c) 5189 (d) 8625
17. 17.What is the smallest number you must take away from 377 so that it divides exactly by 8?
18. 18.How many factors does 85 have?
19. 19.What is the smallest number you must add to 852 so that it divides exactly by 13?
20. 20.Which of these numbers divides exactly by 11? (a) 8315 (b) 8967 (c) 6457 (d) 3585
21. 21.Which of these numbers divides exactly by 4? (a) 4674 (b) 6818 (c) 2248 (d) 9517
22. 22.Which of these numbers divides exactly by 6? (a) 7868 (b) 3146 (c) 6422 (d) 8262
23. 23.What is the smallest number you must take away from 393 so that it divides exactly by 13?
24. 24.What is the smallest number you must add to 987 so that it divides exactly by 8?
25. 25.How many factors does 46 have?
26. 26.What is the smallest number you must take away from 115 so that it divides exactly by 8?
27. 27.How many factors does 75 have?
28. 28.Which of these numbers divides exactly by 8? (a) 8733 (b) 5257 (c) 1392 (d) 3577
29. 29.What is the smallest number you must take away from 766 so that it divides exactly by 12?
30. 30.Which of these numbers divides exactly by 9? (a) 5882 (b) 8966 (c) 6486 (d) 6876
31. 31.What is the smallest number you must add to 677 so that it divides exactly by 3?
32. 32.What is the smallest number you must add to 381 so that it divides exactly by 8?
33. 33.What is the smallest number you must add to 107 so that it divides exactly by 7?
34. 34.Which of these numbers divides exactly by 3? (a) 1573 (b) 6438 (c) 6523 (d) 9163
35. 35.Which of these numbers divides exactly by 6? (a) 2569 (b) 8618 (c) 6020 (d) 3024
36. 36.How many factors does 81 have?
37. 37.What is the smallest number you must add to 245 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 3? (a) 5851 (b) 2209 (c) 7982 (d) 3681
39. 39.What is the smallest number you must take away from 713 so that it divides exactly by 13?
40. 40.Which of these numbers divides exactly by 9? (a) 8333 (b) 9975 (c) 9405 (d) 4466

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