Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 49 · 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.Which of these numbers divides exactly by 8? (a) 3986 (b) 6627 (c) 5338 (d) 7208
2. 2.What is the smallest number you must take away from 114 so that it divides exactly by 4?
3. 3.Which of these numbers divides exactly by 4? (a) 1832 (b) 2894 (c) 2906 (d) 2135
4. 4.What is the smallest number you must take away from 502 so that it divides exactly by 11?
5. 5.Which of these numbers divides exactly by 8? (a) 7437 (b) 3977 (c) 7984 (d) 8010
6. 6.How many factors does 89 have?
7. 7.Which of these numbers divides exactly by 4? (a) 7682 (b) 8197 (c) 2784 (d) 8597
8. 8.Which of these numbers divides exactly by 3? (a) 7585 (b) 7816 (c) 1807 (d) 9564
9. 9.Which of these numbers divides exactly by 4? (a) 6903 (b) 3433 (c) 8968 (d) 6794
10. 10.What is the smallest number you must take away from 235 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 603 so that it divides exactly by 13?
12. 12.How many factors does 88 have?
13. 13.What is the smallest number you must take away from 206 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 642 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 701 so that it divides exactly by 13?
16. 16.What is the smallest number you must take away from 284 so that it divides exactly by 6?
17. 17.How many factors does 25 have?
18. 18.What is the smallest number you must take away from 528 so that it divides exactly by 9?
19. 19.How many factors does 32 have?
20. 20.What is the smallest number you must take away from 272 so that it divides exactly by 13?
21. 21.What is the smallest number you must add to 851 so that it divides exactly by 6?
22. 22.What is the smallest number you must take away from 592 so that it divides exactly by 6?
23. 23.Which of these numbers divides exactly by 8? (a) 2577 (b) 8484 (c) 3528 (d) 8626
24. 24.What is the smallest number you must take away from 431 so that it divides exactly by 3?
25. 25.How many factors does 51 have?
26. 26.What is the smallest number you must take away from 405 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 391 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 380 so that it divides exactly by 9?
29. 29.How many factors does 66 have?
30. 30.What is the smallest number you must take away from 137 so that it divides exactly by 11?
31. 31.Which of these numbers divides exactly by 9? (a) 1481 (b) 1711 (c) 4473 (d) 8311
32. 32.How many factors does 15 have?
33. 33.Which of these numbers divides exactly by 3? (a) 4648 (b) 7408 (c) 9856 (d) 5973
34. 34.What is the smallest number you must take away from 607 so that it divides exactly by 13?
35. 35.How many factors does 85 have?
36. 36.Which of these numbers divides exactly by 4? (a) 9681 (b) 3346 (c) 7864 (d) 8099
37. 37.Which of these numbers divides exactly by 3? (a) 8473 (b) 6690 (c) 6722 (d) 2722
38. 38.What is the smallest number you must take away from 114 so that it divides exactly by 9?
39. 39.How many factors does 78 have?
40. 40.How many factors does 43 have?

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