Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 303 · 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) 7413 (b) 2688 (c) 3217 (d) 1607
2. 2.Which of these numbers divides exactly by 4? (a) 2838 (b) 4124 (c) 5157 (d) 5743
3. 3.What is the smallest number you must take away from 254 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 9? (a) 4509 (b) 7206 (c) 2681 (d) 6914
5. 5.Which of these numbers divides exactly by 3? (a) 9760 (b) 8283 (c) 5101 (d) 9413
6. 6.How many factors does 19 have?
7. 7.What is the smallest number you must take away from 574 so that it divides exactly by 11?
8. 8.How many factors does 40 have?
9. 9.What is the smallest number you must take away from 222 so that it divides exactly by 13?
10. 10.What is the smallest number you must take away from 375 so that it divides exactly by 7?
11. 11.What is the smallest number you must add to 404 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 969 so that it divides exactly by 9?
13. 13.What is the smallest number you must take away from 663 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 173 so that it divides exactly by 8?
15. 15.How many factors does 28 have?
16. 16.What is the smallest number you must add to 121 so that it divides exactly by 3?
17. 17.How many factors does 93 have?
18. 18.What is the smallest number you must add to 731 so that it divides exactly by 4?
19. 19.How many factors does 27 have?
20. 20.What is the smallest number you must add to 156 so that it divides exactly by 8?
21. 21.What is the smallest number you must take away from 610 so that it divides exactly by 12?
22. 22.What is the smallest number you must add to 268 so that it divides exactly by 8?
23. 23.What is the smallest number you must take away from 592 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 6? (a) 6238 (b) 2253 (c) 8898 (d) 2683
25. 25.How many factors does 33 have?
26. 26.Which of these numbers divides exactly by 3? (a) 2767 (b) 6977 (c) 6929 (d) 7539
27. 27.How many factors does 63 have?
28. 28.Which of these numbers divides exactly by 9? (a) 6634 (b) 2133 (c) 1397 (d) 6311
29. 29.How many factors does 81 have?
30. 30.Which of these numbers divides exactly by 8? (a) 1332 (b) 4307 (c) 5835 (d) 5064
31. 31.Which of these numbers divides exactly by 11? (a) 7244 (b) 3599 (c) 8217 (d) 2819
32. 32.How many factors does 29 have?
33. 33.How many factors does 67 have?
34. 34.How many factors does 12 have?
35. 35.What is the smallest number you must take away from 485 so that it divides exactly by 8?
36. 36.What is the smallest number you must take away from 501 so that it divides exactly by 11?
37. 37.What is the smallest number you must add to 994 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 982 so that it divides exactly by 9?
39. 39.Which of these numbers divides exactly by 11? (a) 9838 (b) 2195 (c) 9816 (d) 5016
40. 40.Which of these numbers divides exactly by 3? (a) 3945 (b) 7447 (c) 4697 (d) 3134

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