Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 51 · 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 4? (a) 6459 (b) 2108 (c) 2090 (d) 5246
2. 2.Which of these numbers divides exactly by 3? (a) 1311 (b) 8827 (c) 8194 (d) 1784
3. 3.Which of these numbers divides exactly by 3? (a) 6395 (b) 6333 (c) 6599 (d) 5956
4. 4.Which of these numbers divides exactly by 3? (a) 2593 (b) 7779 (c) 9725 (d) 9088
5. 5.Which of these numbers divides exactly by 8? (a) 4016 (b) 9164 (c) 4586 (d) 7589
6. 6.What is the smallest number you must take away from 607 so that it divides exactly by 8?
7. 7.Which of these numbers divides exactly by 8? (a) 2866 (b) 4473 (c) 7928 (d) 7731
8. 8.What is the smallest number you must take away from 394 so that it divides exactly by 9?
9. 9.Which of these numbers divides exactly by 9? (a) 6134 (b) 2709 (c) 3178 (d) 1661
10. 10.How many factors does 12 have?
11. 11.What is the smallest number you must take away from 374 so that it divides exactly by 4?
12. 12.What is the smallest number you must take away from 868 so that it divides exactly by 13?
13. 13.Which of these numbers divides exactly by 9? (a) 8169 (b) 6753 (c) 9300 (d) 4761
14. 14.What is the smallest number you must take away from 145 so that it divides exactly by 12?
15. 15.What is the smallest number you must add to 585 so that it divides exactly by 4?
16. 16.How many factors does 37 have?
17. 17.What is the smallest number you must add to 494 so that it divides exactly by 4?
18. 18.What is the smallest number you must take away from 497 so that it divides exactly by 11?
19. 19.What is the smallest number you must take away from 624 so that it divides exactly by 9?
20. 20.Which of these numbers divides exactly by 4? (a) 2333 (b) 5332 (c) 2589 (d) 4665
21. 21.What is the smallest number you must add to 341 so that it divides exactly by 4?
22. 22.What is the smallest number you must take away from 463 so that it divides exactly by 12?
23. 23.Which of these numbers divides exactly by 4? (a) 5633 (b) 5508 (c) 3641 (d) 3783
24. 24.How many factors does 54 have?
25. 25.What is the smallest number you must add to 258 so that it divides exactly by 13?
26. 26.What is the smallest number you must add to 501 so that it divides exactly by 4?
27. 27.What is the smallest number you must take away from 388 so that it divides exactly by 8?
28. 28.How many factors does 33 have?
29. 29.How many factors does 87 have?
30. 30.Which of these numbers divides exactly by 8? (a) 5741 (b) 2264 (c) 9145 (d) 1493
31. 31.How many factors does 49 have?
32. 32.What is the smallest number you must take away from 606 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 4? (a) 9206 (b) 1330 (c) 5797 (d) 5676
34. 34.How many factors does 66 have?
35. 35.What is the smallest number you must take away from 783 so that it divides exactly by 13?
36. 36.What is the smallest number you must add to 465 so that it divides exactly by 8?
37. 37.What is the smallest number you must take away from 926 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 671 so that it divides exactly by 6?
39. 39.How many factors does 86 have?
40. 40.How many factors does 34 have?

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