Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 23 · 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 100 have?
2. 2.What is the smallest number you must add to 455 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 868 so that it divides exactly by 11?
4. 4.Which of these numbers divides exactly by 3? (a) 5995 (b) 4792 (c) 3011 (d) 4746
5. 5.What is the smallest number you must add to 314 so that it divides exactly by 13?
6. 6.What is the smallest number you must take away from 988 so that it divides exactly by 9?
7. 7.What is the smallest number you must take away from 300 so that it divides exactly by 8?
8. 8.Which of these numbers divides exactly by 6? (a) 6757 (b) 6612 (c) 3403 (d) 3187
9. 9.How many factors does 14 have?
10. 10.Which of these numbers divides exactly by 3? (a) 4586 (b) 3162 (c) 1343 (d) 1267
11. 11.What is the smallest number you must take away from 213 so that it divides exactly by 8?
12. 12.Which of these numbers divides exactly by 6? (a) 8892 (b) 5234 (c) 4585 (d) 7259
13. 13.What is the smallest number you must add to 544 so that it divides exactly by 13?
14. 14.What is the smallest number you must take away from 577 so that it divides exactly by 8?
15. 15.Which of these numbers divides exactly by 3? (a) 7273 (b) 7130 (c) 8165 (d) 3597
16. 16.What is the smallest number you must add to 808 so that it divides exactly by 12?
17. 17.What is the smallest number you must take away from 106 so that it divides exactly by 12?
18. 18.Which of these numbers divides exactly by 3? (a) 5845 (b) 6705 (c) 7000 (d) 6404
19. 19.How many factors does 41 have?
20. 20.How many factors does 73 have?
21. 21.What is the smallest number you must add to 237 so that it divides exactly by 4?
22. 22.Which of these numbers divides exactly by 9? (a) 4833 (b) 2933 (c) 4452 (d) 1383
23. 23.How many factors does 13 have?
24. 24.What is the smallest number you must take away from 965 so that it divides exactly by 7?
25. 25.Which of these numbers divides exactly by 4? (a) 6552 (b) 2005 (c) 8559 (d) 3594
26. 26.How many factors does 25 have?
27. 27.What is the smallest number you must add to 119 so that it divides exactly by 8?
28. 28.What is the smallest number you must add to 882 so that it divides exactly by 8?
29. 29.How many factors does 35 have?
30. 30.How many factors does 48 have?
31. 31.What is the smallest number you must take away from 761 so that it divides exactly by 11?
32. 32.Which of these numbers divides exactly by 9? (a) 2571 (b) 2295 (c) 3109 (d) 2624
33. 33.How many factors does 29 have?
34. 34.Which of these numbers divides exactly by 11? (a) 8822 (b) 9613 (c) 2485 (d) 7668
35. 35.What is the smallest number you must take away from 214 so that it divides exactly by 9?
36. 36.What is the smallest number you must take away from 721 so that it divides exactly by 4?
37. 37.What is the smallest number you must add to 882 so that it divides exactly by 11?
38. 38.How many factors does 43 have?
39. 39.How many factors does 45 have?
40. 40.How many factors does 86 have?

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