Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 163 · 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 45 have?
2. 2.Which of these numbers divides exactly by 8? (a) 5928 (b) 1122 (c) 8883 (d) 4935
3. 3.How many factors does 70 have?
4. 4.What is the smallest number you must add to 746 so that it divides exactly by 8?
5. 5.What is the smallest number you must take away from 683 so that it divides exactly by 6?
6. 6.What is the smallest number you must take away from 683 so that it divides exactly by 11?
7. 7.Which of these numbers divides exactly by 8? (a) 1777 (b) 9192 (c) 2389 (d) 6116
8. 8.Which of these numbers divides exactly by 6? (a) 4520 (b) 7125 (c) 5646 (d) 7341
9. 9.Which of these numbers divides exactly by 8? (a) 7683 (b) 2303 (c) 1180 (d) 1520
10. 10.Which of these numbers divides exactly by 6? (a) 9373 (b) 3498 (c) 1646 (d) 4072
11. 11.Which of these numbers divides exactly by 4? (a) 6449 (b) 6925 (c) 2778 (d) 5888
12. 12.What is the smallest number you must take away from 169 so that it divides exactly by 7?
13. 13.How many factors does 18 have?
14. 14.What is the smallest number you must take away from 475 so that it divides exactly by 13?
15. 15.Which of these numbers divides exactly by 9? (a) 1994 (b) 2451 (c) 2313 (d) 3713
16. 16.How many factors does 78 have?
17. 17.What is the smallest number you must take away from 988 so that it divides exactly by 3?
18. 18.How many factors does 14 have?
19. 19.How many factors does 84 have?
20. 20.How many factors does 93 have?
21. 21.What is the smallest number you must add to 191 so that it divides exactly by 9?
22. 22.What is the smallest number you must add to 979 so that it divides exactly by 8?
23. 23.How many factors does 67 have?
24. 24.What is the smallest number you must add to 241 so that it divides exactly by 13?
25. 25.Which of these numbers divides exactly by 3? (a) 4530 (b) 2257 (c) 1457 (d) 6682
26. 26.Which of these numbers divides exactly by 9? (a) 4407 (b) 1915 (c) 3347 (d) 2250
27. 27.What is the smallest number you must add to 498 so that it divides exactly by 9?
28. 28.Which of these numbers divides exactly by 11? (a) 2856 (b) 2194 (c) 6043 (d) 6248
29. 29.What is the smallest number you must take away from 823 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 698 so that it divides exactly by 8?
31. 31.What is the smallest number you must add to 335 so that it divides exactly by 4?
32. 32.What is the smallest number you must take away from 181 so that it divides exactly by 3?
33. 33.Which of these numbers divides exactly by 9? (a) 1491 (b) 1469 (c) 1314 (d) 8357
34. 34.What is the smallest number you must take away from 112 so that it divides exactly by 3?
35. 35.How many factors does 79 have?
36. 36.What is the smallest number you must take away from 172 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 321 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 4? (a) 1668 (b) 6985 (c) 5685 (d) 9789
39. 39.Which of these numbers divides exactly by 9? (a) 7420 (b) 8212 (c) 2003 (d) 3096
40. 40.What is the smallest number you must take away from 102 so that it divides exactly by 9?

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