Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 91 · 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 706 so that it divides exactly by 13?
2. 2.How many factors does 79 have?
3. 3.What is the smallest number you must add to 925 so that it divides exactly by 8?
4. 4.What is the smallest number you must add to 170 so that it divides exactly by 13?
5. 5.How many factors does 84 have?
6. 6.Which of these numbers divides exactly by 9? (a) 9081 (b) 1776 (c) 6229 (d) 9574
7. 7.How many factors does 73 have?
8. 8.What is the smallest number you must take away from 653 so that it divides exactly by 8?
9. 9.What is the smallest number you must add to 338 so that it divides exactly by 11?
10. 10.What is the smallest number you must add to 198 so that it divides exactly by 13?
11. 11.How many factors does 57 have?
12. 12.What is the smallest number you must take away from 131 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 348 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 531 so that it divides exactly by 6?
15. 15.What is the smallest number you must add to 401 so that it divides exactly by 12?
16. 16.Which of these numbers divides exactly by 3? (a) 4074 (b) 7027 (c) 2293 (d) 7915
17. 17.What is the smallest number you must add to 157 so that it divides exactly by 8?
18. 18.How many factors does 69 have?
19. 19.What is the smallest number you must add to 415 so that it divides exactly by 9?
20. 20.What is the smallest number you must take away from 584 so that it divides exactly by 9?
21. 21.Which of these numbers divides exactly by 8? (a) 8653 (b) 4728 (c) 5355 (d) 6723
22. 22.How many factors does 50 have?
23. 23.How many factors does 16 have?
24. 24.Which of these numbers divides exactly by 6? (a) 2672 (b) 6264 (c) 9686 (d) 8193
25. 25.What is the smallest number you must add to 196 so that it divides exactly by 3?
26. 26.Which of these numbers divides exactly by 11? (a) 8581 (b) 2637 (c) 3673 (d) 3960
27. 27.Which of these numbers divides exactly by 4? (a) 6345 (b) 9712 (c) 9146 (d) 1378
28. 28.Which of these numbers divides exactly by 8? (a) 2272 (b) 7084 (c) 6591 (d) 7414
29. 29.What is the smallest number you must add to 684 so that it divides exactly by 13?
30. 30.What is the smallest number you must add to 918 so that it divides exactly by 11?
31. 31.How many factors does 18 have?
32. 32.Which of these numbers divides exactly by 11? (a) 6065 (b) 1749 (c) 6481 (d) 6812
33. 33.What is the smallest number you must take away from 184 so that it divides exactly by 7?
34. 34.What is the smallest number you must add to 130 so that it divides exactly by 6?
35. 35.Which of these numbers divides exactly by 3? (a) 2204 (b) 9139 (c) 7618 (d) 7725
36. 36.What is the smallest number you must add to 527 so that it divides exactly by 11?
37. 37.What is the smallest number you must add to 175 so that it divides exactly by 8?
38. 38.How many factors does 43 have?
39. 39.What is the smallest number you must add to 838 so that it divides exactly by 8?
40. 40.Which of these numbers divides exactly by 11? (a) 9251 (b) 2674 (c) 1493 (d) 7833

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