Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 298 · 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 87 have?
2. 2.What is the smallest number you must add to 421 so that it divides exactly by 6?
3. 3.How many factors does 12 have?
4. 4.How many factors does 35 have?
5. 5.Which of these numbers divides exactly by 9? (a) 2160 (b) 8142 (c) 5257 (d) 3310
6. 6.How many factors does 43 have?
7. 7.Which of these numbers divides exactly by 9? (a) 7746 (b) 3118 (c) 3042 (d) 7778
8. 8.Which of these numbers divides exactly by 11? (a) 6087 (b) 5094 (c) 9464 (d) 8767
9. 9.Which of these numbers divides exactly by 4? (a) 1679 (b) 3357 (c) 4426 (d) 1192
10. 10.How many factors does 48 have?
11. 11.How many factors does 34 have?
12. 12.Which of these numbers divides exactly by 6? (a) 8124 (b) 6602 (c) 6436 (d) 6644
13. 13.What is the smallest number you must add to 863 so that it divides exactly by 7?
14. 14.What is the smallest number you must add to 546 so that it divides exactly by 8?
15. 15.Which of these numbers divides exactly by 8? (a) 5583 (b) 2057 (c) 2222 (d) 8600
16. 16.What is the smallest number you must add to 690 so that it divides exactly by 4?
17. 17.Which of these numbers divides exactly by 3? (a) 7465 (b) 2557 (c) 7617 (d) 4324
18. 18.How many factors does 32 have?
19. 19.What is the smallest number you must add to 473 so that it divides exactly by 6?
20. 20.What is the smallest number you must take away from 221 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 8? (a) 6998 (b) 4590 (c) 3051 (d) 2912
22. 22.How many factors does 16 have?
23. 23.Which of these numbers divides exactly by 4? (a) 2098 (b) 9683 (c) 2862 (d) 2216
24. 24.How many factors does 26 have?
25. 25.What is the smallest number you must add to 732 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 469 so that it divides exactly by 11?
27. 27.Which of these numbers divides exactly by 8? (a) 7262 (b) 8311 (c) 9024 (d) 5932
28. 28.What is the smallest number you must add to 641 so that it divides exactly by 4?
29. 29.What is the smallest number you must take away from 754 so that it divides exactly by 6?
30. 30.What is the smallest number you must add to 219 so that it divides exactly by 13?
31. 31.Which of these numbers divides exactly by 3? (a) 1175 (b) 5092 (c) 5300 (d) 5904
32. 32.What is the smallest number you must add to 535 so that it divides exactly by 6?
33. 33.What is the smallest number you must take away from 746 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 851 so that it divides exactly by 12?
35. 35.What is the smallest number you must add to 507 so that it divides exactly by 12?
36. 36.Which of these numbers divides exactly by 11? (a) 2821 (b) 3038 (c) 4806 (d) 8624
37. 37.What is the smallest number you must add to 927 so that it divides exactly by 7?
38. 38.Which of these numbers divides exactly by 8? (a) 6578 (b) 2089 (c) 3888 (d) 9836
39. 39.How many factors does 75 have?
40. 40.What is the smallest number you must take away from 656 so that it divides exactly by 13?

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