Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 2 · 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 21 have?
2. 2.What is the smallest number you must take away from 745 so that it divides exactly by 7?
3. 3.Which of these numbers divides exactly by 8? (a) 9346 (b) 3335 (c) 8280 (d) 2734
4. 4.Which of these numbers divides exactly by 8? (a) 8293 (b) 5691 (c) 8709 (d) 7136
5. 5.How many factors does 52 have?
6. 6.Which of these numbers divides exactly by 4? (a) 3962 (b) 2714 (c) 5538 (d) 6316
7. 7.How many factors does 16 have?
8. 8.How many factors does 19 have?
9. 9.What is the smallest number you must add to 685 so that it divides exactly by 12?
10. 10.What is the smallest number you must add to 943 so that it divides exactly by 3?
11. 11.What is the smallest number you must add to 122 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 6? (a) 8532 (b) 6238 (c) 3202 (d) 8182
13. 13.Which of these numbers divides exactly by 4? (a) 9960 (b) 8071 (c) 2189 (d) 9165
14. 14.Which of these numbers divides exactly by 4? (a) 4275 (b) 8822 (c) 1936 (d) 6121
15. 15.How many factors does 87 have?
16. 16.How many factors does 42 have?
17. 17.What is the smallest number you must take away from 953 so that it divides exactly by 12?
18. 18.What is the smallest number you must take away from 971 so that it divides exactly by 9?
19. 19.How many factors does 13 have?
20. 20.Which of these numbers divides exactly by 6? (a) 2240 (b) 5975 (c) 9138 (d) 5999
21. 21.What is the smallest number you must add to 163 so that it divides exactly by 8?
22. 22.What is the smallest number you must add to 208 so that it divides exactly by 12?
23. 23.What is the smallest number you must add to 502 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 615 so that it divides exactly by 4?
25. 25.Which of these numbers divides exactly by 6? (a) 6440 (b) 3185 (c) 6414 (d) 9021
26. 26.Which of these numbers divides exactly by 11? (a) 6028 (b) 4127 (c) 5253 (d) 8905
27. 27.Which of these numbers divides exactly by 8? (a) 3113 (b) 1900 (c) 3818 (d) 3096
28. 28.Which of these numbers divides exactly by 6? (a) 1494 (b) 3215 (c) 5348 (d) 2815
29. 29.What is the smallest number you must add to 913 so that it divides exactly by 9?
30. 30.Which of these numbers divides exactly by 3? (a) 5567 (b) 7889 (c) 1184 (d) 9447
31. 31.Which of these numbers divides exactly by 3? (a) 2684 (b) 2841 (c) 1048 (d) 5165
32. 32.Which of these numbers divides exactly by 3? (a) 7522 (b) 5102 (c) 3516 (d) 3508
33. 33.What is the smallest number you must add to 786 so that it divides exactly by 12?
34. 34.What is the smallest number you must take away from 534 so that it divides exactly by 9?
35. 35.What is the smallest number you must add to 474 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 815 so that it divides exactly by 9?
37. 37.Which of these numbers divides exactly by 9? (a) 8937 (b) 1864 (c) 9326 (d) 1102
38. 38.What is the smallest number you must add to 584 so that it divides exactly by 13?
39. 39.What is the smallest number you must take away from 639 so that it divides exactly by 8?
40. 40.What is the smallest number you must take away from 269 so that it divides exactly by 6?

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