Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 10 · 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 56 have?
2. 2.How many factors does 29 have?
3. 3.What is the smallest number you must add to 940 so that it divides exactly by 8?
4. 4.What is the smallest number you must add to 245 so that it divides exactly by 9?
5. 5.How many factors does 19 have?
6. 6.Which of these numbers divides exactly by 11? (a) 4466 (b) 1360 (c) 4051 (d) 8873
7. 7.What is the smallest number you must add to 358 so that it divides exactly by 6?
8. 8.How many factors does 47 have?
9. 9.What is the smallest number you must add to 161 so that it divides exactly by 11?
10. 10.Which of these numbers divides exactly by 9? (a) 8818 (b) 9891 (c) 5701 (d) 3963
11. 11.What is the smallest number you must take away from 406 so that it divides exactly by 9?
12. 12.How many factors does 24 have?
13. 13.What is the smallest number you must take away from 164 so that it divides exactly by 13?
14. 14.Which of these numbers divides exactly by 8? (a) 8872 (b) 8948 (c) 5023 (d) 6511
15. 15.How many factors does 15 have?
16. 16.Which of these numbers divides exactly by 6? (a) 8387 (b) 7002 (c) 4712 (d) 9603
17. 17.How many factors does 72 have?
18. 18.Which of these numbers divides exactly by 3? (a) 8707 (b) 5697 (c) 2281 (d) 7834
19. 19.What is the smallest number you must take away from 366 so that it divides exactly by 9?
20. 20.What is the smallest number you must add to 819 so that it divides exactly by 8?
21. 21.Which of these numbers divides exactly by 4? (a) 1853 (b) 2038 (c) 6312 (d) 3965
22. 22.What is the smallest number you must take away from 391 so that it divides exactly by 7?
23. 23.What is the smallest number you must take away from 245 so that it divides exactly by 4?
24. 24.How many factors does 37 have?
25. 25.Which of these numbers divides exactly by 3? (a) 2621 (b) 6207 (c) 3347 (d) 2342
26. 26.What is the smallest number you must take away from 109 so that it divides exactly by 9?
27. 27.How many factors does 43 have?
28. 28.What is the smallest number you must take away from 944 so that it divides exactly by 7?
29. 29.How many factors does 21 have?
30. 30.Which of these numbers divides exactly by 3? (a) 6584 (b) 6468 (c) 7219 (d) 5425
31. 31.What is the smallest number you must take away from 271 so that it divides exactly by 13?
32. 32.Which of these numbers divides exactly by 11? (a) 4746 (b) 1590 (c) 8455 (d) 1254
33. 33.What is the smallest number you must take away from 586 so that it divides exactly by 3?
34. 34.How many factors does 91 have?
35. 35.Which of these numbers divides exactly by 3? (a) 8984 (b) 7664 (c) 6667 (d) 4053
36. 36.Which of these numbers divides exactly by 6? (a) 9555 (b) 7034 (c) 4007 (d) 7788
37. 37.Which of these numbers divides exactly by 3? (a) 7549 (b) 3251 (c) 7807 (d) 7644
38. 38.What is the smallest number you must take away from 688 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 757 so that it divides exactly by 6?
40. 40.How many factors does 61 have?

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