Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 102 · 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.What is the smallest number you must take away from 929 so that it divides exactly by 12?
2. 2.How many factors does 21 have?
3. 3.Which of these numbers divides exactly by 6? (a) 9239 (b) 1764 (c) 1922 (d) 2021
4. 4.What is the smallest number you must take away from 737 so that it divides exactly by 7?
5. 5.What is the smallest number you must take away from 155 so that it divides exactly by 11?
6. 6.How many factors does 36 have?
7. 7.What is the smallest number you must add to 796 so that it divides exactly by 11?
8. 8.Which of these numbers divides exactly by 4? (a) 5771 (b) 1198 (c) 6276 (d) 8890
9. 9.What is the smallest number you must add to 722 so that it divides exactly by 8?
10. 10.What is the smallest number you must add to 827 so that it divides exactly by 4?
11. 11.What is the smallest number you must add to 114 so that it divides exactly by 12?
12. 12.Which of these numbers divides exactly by 3? (a) 6145 (b) 1093 (c) 1213 (d) 6978
13. 13.What is the smallest number you must take away from 322 so that it divides exactly by 3?
14. 14.Which of these numbers divides exactly by 4? (a) 9046 (b) 7547 (c) 4920 (d) 8710
15. 15.What is the smallest number you must add to 557 so that it divides exactly by 4?
16. 16.What is the smallest number you must take away from 139 so that it divides exactly by 8?
17. 17.How many factors does 31 have?
18. 18.How many factors does 26 have?
19. 19.Which of these numbers divides exactly by 4? (a) 2895 (b) 1821 (c) 4232 (d) 3105
20. 20.What is the smallest number you must add to 907 so that it divides exactly by 7?
21. 21.Which of these numbers divides exactly by 11? (a) 6160 (b) 4726 (c) 7308 (d) 1756
22. 22.How many factors does 56 have?
23. 23.What is the smallest number you must add to 683 so that it divides exactly by 4?
24. 24.How many factors does 27 have?
25. 25.Which of these numbers divides exactly by 8? (a) 4972 (b) 3153 (c) 6351 (d) 8040
26. 26.What is the smallest number you must add to 665 so that it divides exactly by 13?
27. 27.How many factors does 49 have?
28. 28.What is the smallest number you must add to 236 so that it divides exactly by 3?
29. 29.What is the smallest number you must take away from 899 so that it divides exactly by 11?
30. 30.How many factors does 55 have?
31. 31.What is the smallest number you must add to 332 so that it divides exactly by 6?
32. 32.What is the smallest number you must take away from 190 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 671 so that it divides exactly by 7?
34. 34.How many factors does 82 have?
35. 35.How many factors does 51 have?
36. 36.How many factors does 96 have?
37. 37.What is the smallest number you must take away from 203 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 6? (a) 3564 (b) 3902 (c) 4221 (d) 9843
39. 39.What is the smallest number you must take away from 119 so that it divides exactly by 13?
40. 40.What is the smallest number you must add to 545 so that it divides exactly by 4?

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