Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 234 · 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 981 so that it divides exactly by 7?
2. 2.How many factors does 24 have?
3. 3.How many factors does 30 have?
4. 4.What is the smallest number you must take away from 269 so that it divides exactly by 3?
5. 5.Which of these numbers divides exactly by 11? (a) 1753 (b) 2574 (c) 6407 (d) 6916
6. 6.What is the smallest number you must add to 576 so that it divides exactly by 7?
7. 7.What is the smallest number you must add to 738 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 914 so that it divides exactly by 8?
9. 9.What is the smallest number you must add to 371 so that it divides exactly by 3?
10. 10.What is the smallest number you must add to 756 so that it divides exactly by 11?
11. 11.What is the smallest number you must take away from 278 so that it divides exactly by 4?
12. 12.How many factors does 73 have?
13. 13.Which of these numbers divides exactly by 4? (a) 5435 (b) 8671 (c) 9729 (d) 7264
14. 14.What is the smallest number you must take away from 907 so that it divides exactly by 3?
15. 15.How many factors does 85 have?
16. 16.Which of these numbers divides exactly by 3? (a) 2960 (b) 6093 (c) 7667 (d) 5857
17. 17.Which of these numbers divides exactly by 3? (a) 5704 (b) 5465 (c) 7341 (d) 3526
18. 18.How many factors does 70 have?
19. 19.Which of these numbers divides exactly by 3? (a) 4939 (b) 9063 (c) 5804 (d) 3875
20. 20.How many factors does 20 have?
21. 21.How many factors does 64 have?
22. 22.How many factors does 17 have?
23. 23.What is the smallest number you must add to 239 so that it divides exactly by 9?
24. 24.What is the smallest number you must add to 951 so that it divides exactly by 9?
25. 25.How many factors does 27 have?
26. 26.Which of these numbers divides exactly by 3? (a) 2474 (b) 1032 (c) 5095 (d) 3367
27. 27.What is the smallest number you must add to 967 so that it divides exactly by 9?
28. 28.Which of these numbers divides exactly by 8? (a) 2141 (b) 7419 (c) 8336 (d) 7148
29. 29.Which of these numbers divides exactly by 9? (a) 8766 (b) 7313 (c) 6071 (d) 2532
30. 30.How many factors does 98 have?
31. 31.What is the smallest number you must take away from 954 so that it divides exactly by 11?
32. 32.What is the smallest number you must take away from 357 so that it divides exactly by 11?
33. 33.What is the smallest number you must take away from 510 so that it divides exactly by 9?
34. 34.How many factors does 37 have?
35. 35.What is the smallest number you must add to 643 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 663 so that it divides exactly by 9?
37. 37.How many factors does 34 have?
38. 38.What is the smallest number you must add to 317 so that it divides exactly by 4?
39. 39.What is the smallest number you must add to 718 so that it divides exactly by 6?
40. 40.Which of these numbers divides exactly by 8? (a) 1873 (b) 9087 (c) 7355 (d) 1992

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