Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 181 · 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 86 have?
2. 2.What is the smallest number you must add to 356 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 949 so that it divides exactly by 8?
4. 4.Which of these numbers divides exactly by 11? (a) 3630 (b) 3961 (c) 1121 (d) 8848
5. 5.Which of these numbers divides exactly by 11? (a) 7399 (b) 6133 (c) 1071 (d) 2013
6. 6.Which of these numbers divides exactly by 3? (a) 1139 (b) 4685 (c) 7549 (d) 5766
7. 7.Which of these numbers divides exactly by 9? (a) 6375 (b) 4009 (c) 2607 (d) 2718
8. 8.How many factors does 80 have?
9. 9.What is the smallest number you must take away from 889 so that it divides exactly by 4?
10. 10.What is the smallest number you must take away from 205 so that it divides exactly by 3?
11. 11.Which of these numbers divides exactly by 6? (a) 7139 (b) 5328 (c) 8609 (d) 4173
12. 12.Which of these numbers divides exactly by 11? (a) 2621 (b) 2512 (c) 5661 (d) 8206
13. 13.What is the smallest number you must add to 729 so that it divides exactly by 4?
14. 14.How many factors does 25 have?
15. 15.What is the smallest number you must take away from 187 so that it divides exactly by 9?
16. 16.What is the smallest number you must take away from 519 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 9? (a) 7065 (b) 1176 (c) 6058 (d) 6514
18. 18.What is the smallest number you must add to 502 so that it divides exactly by 12?
19. 19.Which of these numbers divides exactly by 11? (a) 7548 (b) 3475 (c) 3508 (d) 3388
20. 20.How many factors does 39 have?
21. 21.Which of these numbers divides exactly by 9? (a) 1014 (b) 4228 (c) 1323 (d) 1574
22. 22.What is the smallest number you must take away from 927 so that it divides exactly by 13?
23. 23.How many factors does 46 have?
24. 24.How many factors does 72 have?
25. 25.What is the smallest number you must take away from 145 so that it divides exactly by 4?
26. 26.What is the smallest number you must take away from 167 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 734 so that it divides exactly by 3?
28. 28.What is the smallest number you must take away from 683 so that it divides exactly by 11?
29. 29.How many factors does 66 have?
30. 30.What is the smallest number you must add to 670 so that it divides exactly by 9?
31. 31.How many factors does 21 have?
32. 32.Which of these numbers divides exactly by 9? (a) 8289 (b) 5149 (c) 3038 (d) 6646
33. 33.What is the smallest number you must add to 163 so that it divides exactly by 12?
34. 34.How many factors does 18 have?
35. 35.Which of these numbers divides exactly by 9? (a) 9083 (b) 1878 (c) 7967 (d) 9126
36. 36.What is the smallest number you must add to 586 so that it divides exactly by 9?
37. 37.How many factors does 56 have?
38. 38.Which of these numbers divides exactly by 6? (a) 8394 (b) 5378 (c) 8300 (d) 9353
39. 39.What is the smallest number you must take away from 291 so that it divides exactly by 8?
40. 40.What is the smallest number you must add to 960 so that it divides exactly by 13?

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