Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 117 · 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 79 have?
2. 2.How many factors does 95 have?
3. 3.What is the smallest number you must take away from 362 so that it divides exactly by 4?
4. 4.What is the smallest number you must add to 142 so that it divides exactly by 4?
5. 5.How many factors does 17 have?
6. 6.What is the smallest number you must add to 157 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 6? (a) 9627 (b) 3390 (c) 8200 (d) 5183
8. 8.What is the smallest number you must take away from 626 so that it divides exactly by 4?
9. 9.Which of these numbers divides exactly by 3? (a) 1664 (b) 6094 (c) 7049 (d) 6438
10. 10.Which of these numbers divides exactly by 4? (a) 1146 (b) 7870 (c) 2588 (d) 2273
11. 11.Which of these numbers divides exactly by 6? (a) 9766 (b) 9979 (c) 7563 (d) 3054
12. 12.Which of these numbers divides exactly by 6? (a) 8581 (b) 3012 (c) 4109 (d) 3977
13. 13.What is the smallest number you must add to 426 so that it divides exactly by 12?
14. 14.How many factors does 55 have?
15. 15.What is the smallest number you must take away from 137 so that it divides exactly by 9?
16. 16.Which of these numbers divides exactly by 9? (a) 9762 (b) 8694 (c) 6196 (d) 8942
17. 17.What is the smallest number you must add to 810 so that it divides exactly by 4?
18. 18.How many factors does 32 have?
19. 19.Which of these numbers divides exactly by 11? (a) 6027 (b) 9165 (c) 6779 (d) 9713
20. 20.What is the smallest number you must take away from 416 so that it divides exactly by 11?
21. 21.How many factors does 46 have?
22. 22.Which of these numbers divides exactly by 11? (a) 7607 (b) 2387 (c) 9545 (d) 1013
23. 23.What is the smallest number you must add to 163 so that it divides exactly by 13?
24. 24.What is the smallest number you must take away from 815 so that it divides exactly by 3?
25. 25.How many factors does 34 have?
26. 26.What is the smallest number you must take away from 219 so that it divides exactly by 6?
27. 27.How many factors does 30 have?
28. 28.What is the smallest number you must take away from 566 so that it divides exactly by 13?
29. 29.How many factors does 70 have?
30. 30.What is the smallest number you must take away from 570 so that it divides exactly by 12?
31. 31.How many factors does 72 have?
32. 32.What is the smallest number you must take away from 127 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 159 so that it divides exactly by 9?
34. 34.Which of these numbers divides exactly by 6? (a) 2497 (b) 1831 (c) 2386 (d) 7464
35. 35.What is the smallest number you must take away from 298 so that it divides exactly by 9?
36. 36.Which of these numbers divides exactly by 6? (a) 5387 (b) 5468 (c) 9369 (d) 5790
37. 37.How many factors does 60 have?
38. 38.What is the smallest number you must take away from 532 so that it divides exactly by 6?
39. 39.What is the smallest number you must take away from 790 so that it divides exactly by 9?
40. 40.Which of these numbers divides exactly by 11? (a) 2379 (b) 2924 (c) 8221 (d) 3586

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