Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 192 · 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 662 so that it divides exactly by 4?
2. 2.How many factors does 75 have?
3. 3.Which of these numbers divides exactly by 11? (a) 7260 (b) 6954 (c) 5199 (d) 8560
4. 4.How many factors does 83 have?
5. 5.How many factors does 31 have?
6. 6.What is the smallest number you must add to 346 so that it divides exactly by 6?
7. 7.What is the smallest number you must take away from 449 so that it divides exactly by 6?
8. 8.How many factors does 95 have?
9. 9.What is the smallest number you must add to 856 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 557 so that it divides exactly by 9?
11. 11.Which of these numbers divides exactly by 6? (a) 3603 (b) 8602 (c) 8202 (d) 9111
12. 12.How many factors does 19 have?
13. 13.What is the smallest number you must add to 220 so that it divides exactly by 3?
14. 14.What is the smallest number you must take away from 136 so that it divides exactly by 9?
15. 15.What is the smallest number you must take away from 678 so that it divides exactly by 13?
16. 16.What is the smallest number you must take away from 769 so that it divides exactly by 4?
17. 17.Which of these numbers divides exactly by 3? (a) 9649 (b) 4300 (c) 3471 (d) 6323
18. 18.Which of these numbers divides exactly by 8? (a) 8754 (b) 4183 (c) 2995 (d) 6696
19. 19.How many factors does 56 have?
20. 20.What is the smallest number you must take away from 142 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 449 so that it divides exactly by 8?
22. 22.What is the smallest number you must add to 758 so that it divides exactly by 4?
23. 23.What is the smallest number you must take away from 549 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 3? (a) 2084 (b) 3431 (c) 8100 (d) 4783
25. 25.How many factors does 20 have?
26. 26.What is the smallest number you must add to 879 so that it divides exactly by 11?
27. 27.How many factors does 85 have?
28. 28.Which of these numbers divides exactly by 9? (a) 9326 (b) 8441 (c) 2015 (d) 5823
29. 29.What is the smallest number you must add to 712 so that it divides exactly by 3?
30. 30.Which of these numbers divides exactly by 11? (a) 7687 (b) 7251 (c) 4517 (d) 6765
31. 31.How many factors does 46 have?
32. 32.What is the smallest number you must take away from 239 so that it divides exactly by 7?
33. 33.Which of these numbers divides exactly by 4? (a) 7076 (b) 9666 (c) 3777 (d) 1455
34. 34.How many factors does 15 have?
35. 35.What is the smallest number you must take away from 134 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 4? (a) 6622 (b) 9112 (c) 3491 (d) 8366
37. 37.How many factors does 37 have?
38. 38.How many factors does 86 have?
39. 39.Which of these numbers divides exactly by 8? (a) 4427 (b) 6727 (c) 3208 (d) 7126
40. 40.Which of these numbers divides exactly by 4? (a) 6143 (b) 7323 (c) 6496 (d) 7881

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