Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 34 · 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 701 so that it divides exactly by 9?
2. 2.How many factors does 34 have?
3. 3.Which of these numbers divides exactly by 6? (a) 5537 (b) 3577 (c) 7323 (d) 1764
4. 4.What is the smallest number you must add to 371 so that it divides exactly by 4?
5. 5.What is the smallest number you must take away from 523 so that it divides exactly by 11?
6. 6.How many factors does 94 have?
7. 7.What is the smallest number you must add to 668 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 185 so that it divides exactly by 9?
9. 9.What is the smallest number you must take away from 393 so that it divides exactly by 6?
10. 10.How many factors does 61 have?
11. 11.What is the smallest number you must add to 318 so that it divides exactly by 4?
12. 12.How many factors does 17 have?
13. 13.What is the smallest number you must add to 284 so that it divides exactly by 6?
14. 14.Which of these numbers divides exactly by 11? (a) 3892 (b) 2906 (c) 3220 (d) 4906
15. 15.How many factors does 44 have?
16. 16.What is the smallest number you must add to 928 so that it divides exactly by 12?
17. 17.What is the smallest number you must add to 946 so that it divides exactly by 12?
18. 18.How many factors does 50 have?
19. 19.What is the smallest number you must add to 766 so that it divides exactly by 11?
20. 20.How many factors does 97 have?
21. 21.Which of these numbers divides exactly by 6? (a) 5132 (b) 2077 (c) 7391 (d) 8802
22. 22.What is the smallest number you must add to 254 so that it divides exactly by 6?
23. 23.How many factors does 41 have?
24. 24.What is the smallest number you must take away from 438 so that it divides exactly by 9?
25. 25.How many factors does 47 have?
26. 26.What is the smallest number you must take away from 546 so that it divides exactly by 8?
27. 27.Which of these numbers divides exactly by 6? (a) 7742 (b) 2965 (c) 8520 (d) 5942
28. 28.What is the smallest number you must add to 125 so that it divides exactly by 11?
29. 29.How many factors does 58 have?
30. 30.Which of these numbers divides exactly by 11? (a) 2559 (b) 5544 (c) 4959 (d) 4770
31. 31.What is the smallest number you must add to 968 so that it divides exactly by 13?
32. 32.What is the smallest number you must take away from 916 so that it divides exactly by 8?
33. 33.What is the smallest number you must take away from 482 so that it divides exactly by 8?
34. 34.What is the smallest number you must take away from 163 so that it divides exactly by 4?
35. 35.How many factors does 23 have?
36. 36.How many factors does 67 have?
37. 37.Which of these numbers divides exactly by 4? (a) 3605 (b) 9928 (c) 1195 (d) 8338
38. 38.What is the smallest number you must add to 100 so that it divides exactly by 9?
39. 39.Which of these numbers divides exactly by 3? (a) 5138 (b) 2519 (c) 3322 (d) 7332
40. 40.What is the smallest number you must take away from 981 so that it divides exactly by 7?

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