Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 194 · 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 24 have?
2. 2.How many factors does 75 have?
3. 3.How many factors does 77 have?
4. 4.What is the smallest number you must add to 126 so that it divides exactly by 8?
5. 5.Which of these numbers divides exactly by 8? (a) 1260 (b) 4494 (c) 6272 (d) 6585
6. 6.Which of these numbers divides exactly by 8? (a) 8103 (b) 1160 (c) 4092 (d) 7745
7. 7.Which of these numbers divides exactly by 3? (a) 4946 (b) 1307 (c) 1375 (d) 3027
8. 8.What is the smallest number you must add to 415 so that it divides exactly by 4?
9. 9.What is the smallest number you must add to 570 so that it divides exactly by 4?
10. 10.Which of these numbers divides exactly by 4? (a) 4973 (b) 2469 (c) 3484 (d) 6165
11. 11.How many factors does 65 have?
12. 12.How many factors does 91 have?
13. 13.What is the smallest number you must add to 583 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 901 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 844 so that it divides exactly by 9?
16. 16.What is the smallest number you must add to 375 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 6? (a) 8253 (b) 4081 (c) 5242 (d) 1590
18. 18.How many factors does 17 have?
19. 19.What is the smallest number you must take away from 410 so that it divides exactly by 4?
20. 20.What is the smallest number you must take away from 820 so that it divides exactly by 9?
21. 21.What is the smallest number you must take away from 797 so that it divides exactly by 13?
22. 22.What is the smallest number you must take away from 572 so that it divides exactly by 9?
23. 23.What is the smallest number you must take away from 114 so that it divides exactly by 7?
24. 24.What is the smallest number you must take away from 838 so that it divides exactly by 4?
25. 25.Which of these numbers divides exactly by 8? (a) 9552 (b) 8421 (c) 7051 (d) 3882
26. 26.How many factors does 23 have?
27. 27.What is the smallest number you must add to 161 so that it divides exactly by 3?
28. 28.What is the smallest number you must add to 463 so that it divides exactly by 11?
29. 29.What is the smallest number you must take away from 182 so that it divides exactly by 9?
30. 30.What is the smallest number you must take away from 613 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 3? (a) 1303 (b) 4389 (c) 1019 (d) 1571
32. 32.How many factors does 60 have?
33. 33.How many factors does 66 have?
34. 34.Which of these numbers divides exactly by 9? (a) 2349 (b) 8700 (c) 8113 (d) 3306
35. 35.What is the smallest number you must add to 724 so that it divides exactly by 8?
36. 36.What is the smallest number you must take away from 806 so that it divides exactly by 7?
37. 37.Which of these numbers divides exactly by 3? (a) 8848 (b) 5330 (c) 3258 (d) 4790
38. 38.How many factors does 27 have?
39. 39.What is the smallest number you must add to 314 so that it divides exactly by 4?
40. 40.What is the smallest number you must add to 922 so that it divides exactly by 12?

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