Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 18 · 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 194 so that it divides exactly by 9?
2. 2.How many factors does 25 have?
3. 3.What is the smallest number you must add to 422 so that it divides exactly by 11?
4. 4.What is the smallest number you must add to 383 so that it divides exactly by 7?
5. 5.Which of these numbers divides exactly by 11? (a) 3228 (b) 3619 (c) 9090 (d) 6720
6. 6.Which of these numbers divides exactly by 9? (a) 6445 (b) 9398 (c) 5742 (d) 2069
7. 7.Which of these numbers divides exactly by 4? (a) 1841 (b) 2070 (c) 7484 (d) 2059
8. 8.What is the smallest number you must take away from 316 so that it divides exactly by 13?
9. 9.How many factors does 52 have?
10. 10.Which of these numbers divides exactly by 3? (a) 9160 (b) 3525 (c) 8918 (d) 1183
11. 11.How many factors does 93 have?
12. 12.Which of these numbers divides exactly by 3? (a) 2056 (b) 1079 (c) 1554 (d) 7000
13. 13.What is the smallest number you must add to 934 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 737 so that it divides exactly by 12?
15. 15.Which of these numbers divides exactly by 4? (a) 2613 (b) 5855 (c) 3468 (d) 5609
16. 16.What is the smallest number you must take away from 269 so that it divides exactly by 6?
17. 17.What is the smallest number you must take away from 694 so that it divides exactly by 12?
18. 18.How many factors does 17 have?
19. 19.Which of these numbers divides exactly by 4? (a) 9905 (b) 4509 (c) 5894 (d) 5248
20. 20.How many factors does 85 have?
21. 21.Which of these numbers divides exactly by 8? (a) 6098 (b) 8551 (c) 1984 (d) 3258
22. 22.Which of these numbers divides exactly by 4? (a) 3784 (b) 3374 (c) 6749 (d) 3117
23. 23.How many factors does 98 have?
24. 24.What is the smallest number you must add to 402 so that it divides exactly by 7?
25. 25.What is the smallest number you must add to 835 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 638 so that it divides exactly by 6?
27. 27.What is the smallest number you must add to 516 so that it divides exactly by 9?
28. 28.What is the smallest number you must add to 201 so that it divides exactly by 4?
29. 29.How many factors does 92 have?
30. 30.What is the smallest number you must add to 454 so that it divides exactly by 11?
31. 31.How many factors does 89 have?
32. 32.What is the smallest number you must add to 197 so that it divides exactly by 4?
33. 33.How many factors does 42 have?
34. 34.How many factors does 31 have?
35. 35.What is the smallest number you must take away from 281 so that it divides exactly by 6?
36. 36.What is the smallest number you must add to 496 so that it divides exactly by 7?
37. 37.How many factors does 38 have?
38. 38.Which of these numbers divides exactly by 8? (a) 8680 (b) 3788 (c) 6292 (d) 8660
39. 39.What is the smallest number you must add to 755 so that it divides exactly by 13?
40. 40.How many factors does 24 have?

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