Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 296 · 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 91 have?
2. 2.How many factors does 59 have?
3. 3.What is the smallest number you must take away from 646 so that it divides exactly by 3?
4. 4.Which of these numbers divides exactly by 3? (a) 9093 (b) 9823 (c) 4270 (d) 6550
5. 5.What is the smallest number you must take away from 741 so that it divides exactly by 6?
6. 6.Which of these numbers divides exactly by 9? (a) 3032 (b) 7137 (c) 7975 (d) 2940
7. 7.What is the smallest number you must take away from 398 so that it divides exactly by 13?
8. 8.How many factors does 32 have?
9. 9.How many factors does 81 have?
10. 10.What is the smallest number you must take away from 700 so that it divides exactly by 13?
11. 11.How many factors does 19 have?
12. 12.Which of these numbers divides exactly by 3? (a) 6628 (b) 7047 (c) 4126 (d) 9892
13. 13.What is the smallest number you must add to 202 so that it divides exactly by 13?
14. 14.How many factors does 51 have?
15. 15.How many factors does 18 have?
16. 16.What is the smallest number you must take away from 982 so that it divides exactly by 3?
17. 17.What is the smallest number you must take away from 794 so that it divides exactly by 11?
18. 18.What is the smallest number you must add to 599 so that it divides exactly by 6?
19. 19.What is the smallest number you must add to 636 so that it divides exactly by 8?
20. 20.What is the smallest number you must add to 467 so that it divides exactly by 3?
21. 21.Which of these numbers divides exactly by 6? (a) 8153 (b) 4396 (c) 2461 (d) 5850
22. 22.Which of these numbers divides exactly by 4? (a) 6108 (b) 3659 (c) 7894 (d) 9835
23. 23.What is the smallest number you must take away from 874 so that it divides exactly by 12?
24. 24.How many factors does 77 have?
25. 25.How many factors does 93 have?
26. 26.What is the smallest number you must add to 127 so that it divides exactly by 4?
27. 27.Which of these numbers divides exactly by 3? (a) 2095 (b) 8868 (c) 9760 (d) 5482
28. 28.How many factors does 15 have?
29. 29.What is the smallest number you must add to 695 so that it divides exactly by 8?
30. 30.What is the smallest number you must take away from 574 so that it divides exactly by 8?
31. 31.Which of these numbers divides exactly by 8? (a) 8594 (b) 1088 (c) 9750 (d) 3257
32. 32.What is the smallest number you must take away from 404 so that it divides exactly by 6?
33. 33.How many factors does 96 have?
34. 34.Which of these numbers divides exactly by 9? (a) 3959 (b) 3366 (c) 3841 (d) 4028
35. 35.What is the smallest number you must take away from 276 so that it divides exactly by 8?
36. 36.What is the smallest number you must take away from 469 so that it divides exactly by 12?
37. 37.What is the smallest number you must take away from 877 so that it divides exactly by 3?
38. 38.Which of these numbers divides exactly by 3? (a) 2571 (b) 8164 (c) 4528 (d) 8227
39. 39.What is the smallest number you must take away from 742 so that it divides exactly by 4?
40. 40.What is the smallest number you must take away from 308 so that it divides exactly by 9?

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