Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 291 · 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 43 have?
2. 2.What is the smallest number you must add to 853 so that it divides exactly by 6?
3. 3.How many factors does 40 have?
4. 4.How many factors does 30 have?
5. 5.Which of these numbers divides exactly by 6? (a) 3226 (b) 2950 (c) 1308 (d) 4905
6. 6.Which of these numbers divides exactly by 6? (a) 7557 (b) 9836 (c) 3448 (d) 5760
7. 7.What is the smallest number you must take away from 422 so that it divides exactly by 8?
8. 8.What is the smallest number you must take away from 785 so that it divides exactly by 13?
9. 9.How many factors does 21 have?
10. 10.What is the smallest number you must add to 687 so that it divides exactly by 11?
11. 11.How many factors does 24 have?
12. 12.Which of these numbers divides exactly by 6? (a) 4741 (b) 2737 (c) 1926 (d) 8336
13. 13.What is the smallest number you must add to 341 so that it divides exactly by 3?
14. 14.What is the smallest number you must take away from 683 so that it divides exactly by 13?
15. 15.What is the smallest number you must add to 737 so that it divides exactly by 6?
16. 16.What is the smallest number you must take away from 969 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 4? (a) 3629 (b) 5833 (c) 7703 (d) 1276
18. 18.What is the smallest number you must take away from 337 so that it divides exactly by 11?
19. 19.Which of these numbers divides exactly by 6? (a) 3033 (b) 4904 (c) 8737 (d) 7740
20. 20.How many factors does 54 have?
21. 21.What is the smallest number you must add to 186 so that it divides exactly by 9?
22. 22.Which of these numbers divides exactly by 8? (a) 3007 (b) 1768 (c) 6002 (d) 7054
23. 23.Which of these numbers divides exactly by 6? (a) 6866 (b) 4950 (c) 3699 (d) 4899
24. 24.What is the smallest number you must take away from 708 so that it divides exactly by 11?
25. 25.Which of these numbers divides exactly by 3? (a) 6573 (b) 8879 (c) 7841 (d) 1309
26. 26.What is the smallest number you must take away from 465 so that it divides exactly by 8?
27. 27.How many factors does 51 have?
28. 28.Which of these numbers divides exactly by 9? (a) 1742 (b) 1968 (c) 1710 (d) 2681
29. 29.What is the smallest number you must take away from 177 so that it divides exactly by 4?
30. 30.What is the smallest number you must add to 831 so that it divides exactly by 6?
31. 31.How many factors does 84 have?
32. 32.Which of these numbers divides exactly by 8? (a) 1313 (b) 3928 (c) 1804 (d) 8297
33. 33.What is the smallest number you must add to 233 so that it divides exactly by 13?
34. 34.How many factors does 14 have?
35. 35.What is the smallest number you must add to 901 so that it divides exactly by 12?
36. 36.Which of these numbers divides exactly by 4? (a) 3235 (b) 9196 (c) 1042 (d) 4902
37. 37.How many factors does 80 have?
38. 38.Which of these numbers divides exactly by 8? (a) 8932 (b) 6440 (c) 9934 (d) 2843
39. 39.How many factors does 44 have?
40. 40.How many factors does 76 have?

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