Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 335 · 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 28 have?
2. 2.What is the smallest number you must take away from 266 so that it divides exactly by 11?
3. 3.What is the smallest number you must take away from 359 so that it divides exactly by 3?
4. 4.What is the smallest number you must take away from 173 so that it divides exactly by 4?
5. 5.Which of these numbers divides exactly by 3? (a) 3713 (b) 9581 (c) 1269 (d) 4220
6. 6.What is the smallest number you must take away from 710 so that it divides exactly by 11?
7. 7.How many factors does 85 have?
8. 8.Which of these numbers divides exactly by 4? (a) 8748 (b) 9530 (c) 6151 (d) 1675
9. 9.How many factors does 55 have?
10. 10.Which of these numbers divides exactly by 9? (a) 4024 (b) 1319 (c) 4770 (d) 3500
11. 11.What is the smallest number you must take away from 399 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 8? (a) 5113 (b) 1855 (c) 9481 (d) 2808
13. 13.Which of these numbers divides exactly by 4? (a) 7649 (b) 1248 (c) 7623 (d) 4709
14. 14.Which of these numbers divides exactly by 4? (a) 7151 (b) 5340 (c) 6830 (d) 8077
15. 15.How many factors does 22 have?
16. 16.Which of these numbers divides exactly by 6? (a) 2641 (b) 3636 (c) 1775 (d) 6843
17. 17.What is the smallest number you must take away from 337 so that it divides exactly by 11?
18. 18.Which of these numbers divides exactly by 3? (a) 4586 (b) 4657 (c) 5330 (d) 8595
19. 19.What is the smallest number you must take away from 116 so that it divides exactly by 9?
20. 20.What is the smallest number you must add to 586 so that it divides exactly by 8?
21. 21.What is the smallest number you must add to 853 so that it divides exactly by 8?
22. 22.How many factors does 18 have?
23. 23.What is the smallest number you must add to 606 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 671 so that it divides exactly by 7?
25. 25.Which of these numbers divides exactly by 9? (a) 2167 (b) 1395 (c) 4591 (d) 4736
26. 26.What is the smallest number you must add to 330 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 193 so that it divides exactly by 8?
28. 28.What is the smallest number you must add to 405 so that it divides exactly by 13?
29. 29.What is the smallest number you must add to 322 so that it divides exactly by 3?
30. 30.How many factors does 69 have?
31. 31.What is the smallest number you must add to 772 so that it divides exactly by 3?
32. 32.What is the smallest number you must add to 607 so that it divides exactly by 3?
33. 33.Which of these numbers divides exactly by 6? (a) 4149 (b) 5953 (c) 1512 (d) 9605
34. 34.How many factors does 46 have?
35. 35.How many factors does 86 have?
36. 36.Which of these numbers divides exactly by 11? (a) 3212 (b) 9198 (c) 3790 (d) 6344
37. 37.What is the smallest number you must add to 883 so that it divides exactly by 7?
38. 38.What is the smallest number you must add to 501 so that it divides exactly by 6?
39. 39.How many factors does 24 have?
40. 40.What is the smallest number you must add to 595 so that it divides exactly by 8?

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