Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 319 · 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.Which of these numbers divides exactly by 9? (a) 7225 (b) 1121 (c) 3330 (d) 3131
2. 2.What is the smallest number you must take away from 766 so that it divides exactly by 3?
3. 3.How many factors does 49 have?
4. 4.What is the smallest number you must take away from 846 so that it divides exactly by 7?
5. 5.How many factors does 53 have?
6. 6.Which of these numbers divides exactly by 3? (a) 8260 (b) 2608 (c) 7859 (d) 8703
7. 7.What is the smallest number you must take away from 543 so that it divides exactly by 9?
8. 8.How many factors does 62 have?
9. 9.Which of these numbers divides exactly by 4? (a) 5783 (b) 2263 (c) 7702 (d) 8244
10. 10.How many factors does 38 have?
11. 11.Which of these numbers divides exactly by 8? (a) 9391 (b) 5928 (c) 9609 (d) 3105
12. 12.Which of these numbers divides exactly by 9? (a) 7466 (b) 4381 (c) 3672 (d) 9883
13. 13.What is the smallest number you must take away from 166 so that it divides exactly by 11?
14. 14.Which of these numbers divides exactly by 6? (a) 1249 (b) 2376 (c) 3785 (d) 3481
15. 15.Which of these numbers divides exactly by 8? (a) 6520 (b) 5351 (c) 9171 (d) 1849
16. 16.Which of these numbers divides exactly by 3? (a) 8398 (b) 6418 (c) 1794 (d) 5030
17. 17.What is the smallest number you must take away from 292 so that it divides exactly by 11?
18. 18.Which of these numbers divides exactly by 8? (a) 3622 (b) 6041 (c) 2672 (d) 5883
19. 19.How many factors does 72 have?
20. 20.How many factors does 86 have?
21. 21.What is the smallest number you must take away from 921 so that it divides exactly by 7?
22. 22.Which of these numbers divides exactly by 6? (a) 4846 (b) 1170 (c) 3892 (d) 1748
23. 23.What is the smallest number you must take away from 179 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 131 so that it divides exactly by 6?
25. 25.Which of these numbers divides exactly by 8? (a) 3600 (b) 9697 (c) 3940 (d) 9333
26. 26.Which of these numbers divides exactly by 4? (a) 2746 (b) 7883 (c) 2140 (d) 2347
27. 27.What is the smallest number you must take away from 354 so that it divides exactly by 13?
28. 28.What is the smallest number you must add to 436 so that it divides exactly by 6?
29. 29.What is the smallest number you must take away from 767 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 267 so that it divides exactly by 4?
31. 31.How many factors does 76 have?
32. 32.How many factors does 41 have?
33. 33.What is the smallest number you must add to 185 so that it divides exactly by 4?
34. 34.What is the smallest number you must add to 159 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 4? (a) 7191 (b) 1456 (c) 1079 (d) 6019
36. 36.What is the smallest number you must add to 381 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 579 so that it divides exactly by 8?
38. 38.Which of these numbers divides exactly by 6? (a) 7992 (b) 2639 (c) 7225 (d) 9337
39. 39.Which of these numbers divides exactly by 8? (a) 6179 (b) 3222 (c) 4455 (d) 3208
40. 40.What is the smallest number you must take away from 232 so that it divides exactly by 13?

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