Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 78 · 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 533 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 850 so that it divides exactly by 4?
3. 3.Which of these numbers divides exactly by 4? (a) 4708 (b) 8455 (c) 5398 (d) 9946
4. 4.What is the smallest number you must add to 320 so that it divides exactly by 13?
5. 5.What is the smallest number you must add to 371 so that it divides exactly by 3?
6. 6.Which of these numbers divides exactly by 11? (a) 9423 (b) 9337 (c) 5951 (d) 5034
7. 7.What is the smallest number you must add to 617 so that it divides exactly by 11?
8. 8.Which of these numbers divides exactly by 4? (a) 9387 (b) 3294 (c) 6950 (d) 8304
9. 9.Which of these numbers divides exactly by 4? (a) 4131 (b) 1595 (c) 7857 (d) 9776
10. 10.Which of these numbers divides exactly by 3? (a) 3916 (b) 1598 (c) 3695 (d) 4047
11. 11.How many factors does 58 have?
12. 12.Which of these numbers divides exactly by 3? (a) 8960 (b) 3326 (c) 7662 (d) 2209
13. 13.How many factors does 72 have?
14. 14.Which of these numbers divides exactly by 3? (a) 7698 (b) 9838 (c) 7021 (d) 5657
15. 15.What is the smallest number you must take away from 249 so that it divides exactly by 7?
16. 16.Which of these numbers divides exactly by 11? (a) 1760 (b) 5601 (c) 8654 (d) 7189
17. 17.Which of these numbers divides exactly by 11? (a) 6699 (b) 1640 (c) 9100 (d) 6583
18. 18.How many factors does 27 have?
19. 19.What is the smallest number you must add to 523 so that it divides exactly by 6?
20. 20.How many factors does 25 have?
21. 21.Which of these numbers divides exactly by 3? (a) 3506 (b) 6203 (c) 8730 (d) 6331
22. 22.Which of these numbers divides exactly by 3? (a) 5653 (b) 4888 (c) 4049 (d) 5409
23. 23.How many factors does 13 have?
24. 24.What is the smallest number you must add to 992 so that it divides exactly by 9?
25. 25.How many factors does 32 have?
26. 26.How many factors does 57 have?
27. 27.Which of these numbers divides exactly by 4? (a) 4602 (b) 1082 (c) 6920 (d) 5934
28. 28.How many factors does 14 have?
29. 29.How many factors does 17 have?
30. 30.Which of these numbers divides exactly by 11? (a) 5687 (b) 8461 (c) 2008 (d) 6489
31. 31.What is the smallest number you must add to 130 so that it divides exactly by 3?
32. 32.Which of these numbers divides exactly by 4? (a) 5167 (b) 7791 (c) 1442 (d) 3536
33. 33.Which of these numbers divides exactly by 3? (a) 7661 (b) 1051 (c) 5289 (d) 7231
34. 34.What is the smallest number you must take away from 251 so that it divides exactly by 4?
35. 35.What is the smallest number you must add to 305 so that it divides exactly by 4?
36. 36.How many factors does 100 have?
37. 37.What is the smallest number you must add to 907 so that it divides exactly by 12?
38. 38.What is the smallest number you must take away from 658 so that it divides exactly by 8?
39. 39.What is the smallest number you must add to 512 so that it divides exactly by 9?
40. 40.How many factors does 61 have?

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