Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 109 · 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 22 have?
2. 2.What is the smallest number you must add to 240 so that it divides exactly by 13?
3. 3.What is the smallest number you must add to 283 so that it divides exactly by 12?
4. 4.What is the smallest number you must add to 154 so that it divides exactly by 6?
5. 5.Which of these numbers divides exactly by 4? (a) 2587 (b) 7054 (c) 9314 (d) 4348
6. 6.What is the smallest number you must add to 731 so that it divides exactly by 4?
7. 7.What is the smallest number you must add to 397 so that it divides exactly by 4?
8. 8.What is the smallest number you must take away from 376 so that it divides exactly by 6?
9. 9.How many factors does 15 have?
10. 10.What is the smallest number you must take away from 964 so that it divides exactly by 13?
11. 11.Which of these numbers divides exactly by 3? (a) 2188 (b) 8054 (c) 5796 (d) 4478
12. 12.How many factors does 76 have?
13. 13.What is the smallest number you must add to 883 so that it divides exactly by 13?
14. 14.Which of these numbers divides exactly by 9? (a) 6962 (b) 6049 (c) 8325 (d) 7622
15. 15.What is the smallest number you must take away from 400 so that it divides exactly by 11?
16. 16.Which of these numbers divides exactly by 11? (a) 6611 (b) 2051 (c) 8079 (d) 8980
17. 17.How many factors does 37 have?
18. 18.What is the smallest number you must take away from 454 so that it divides exactly by 8?
19. 19.What is the smallest number you must add to 400 so that it divides exactly by 7?
20. 20.Which of these numbers divides exactly by 9? (a) 3957 (b) 1267 (c) 1969 (d) 6984
21. 21.What is the smallest number you must add to 245 so that it divides exactly by 8?
22. 22.What is the smallest number you must add to 195 so that it divides exactly by 8?
23. 23.Which of these numbers divides exactly by 11? (a) 5236 (b) 6088 (c) 2902 (d) 3899
24. 24.How many factors does 44 have?
25. 25.Which of these numbers divides exactly by 9? (a) 1902 (b) 1043 (c) 6543 (d) 6094
26. 26.How many factors does 25 have?
27. 27.How many factors does 53 have?
28. 28.Which of these numbers divides exactly by 8? (a) 4993 (b) 4110 (c) 2613 (d) 6528
29. 29.How many factors does 74 have?
30. 30.What is the smallest number you must take away from 634 so that it divides exactly by 13?
31. 31.What is the smallest number you must take away from 291 so that it divides exactly by 13?
32. 32.Which of these numbers divides exactly by 4? (a) 9222 (b) 2415 (c) 7325 (d) 8808
33. 33.What is the smallest number you must take away from 121 so that it divides exactly by 4?
34. 34.What is the smallest number you must add to 987 so that it divides exactly by 4?
35. 35.How many factors does 28 have?
36. 36.How many factors does 96 have?
37. 37.Which of these numbers divides exactly by 6? (a) 1474 (b) 1988 (c) 9810 (d) 5440
38. 38.Which of these numbers divides exactly by 8? (a) 4754 (b) 1514 (c) 4296 (d) 4991
39. 39.What is the smallest number you must take away from 388 so that it divides exactly by 12?
40. 40.Which of these numbers divides exactly by 11? (a) 7018 (b) 2252 (c) 4487 (d) 1610

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