Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 101 · 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 92 have?
2. 2.What is the smallest number you must take away from 974 so that it divides exactly by 4?
3. 3.What is the smallest number you must add to 767 so that it divides exactly by 12?
4. 4.What is the smallest number you must add to 868 so that it divides exactly by 13?
5. 5.How many factors does 37 have?
6. 6.What is the smallest number you must add to 559 so that it divides exactly by 3?
7. 7.What is the smallest number you must add to 121 so that it divides exactly by 12?
8. 8.How many factors does 38 have?
9. 9.Which of these numbers divides exactly by 8? (a) 8888 (b) 3822 (c) 3635 (d) 4647
10. 10.What is the smallest number you must take away from 109 so that it divides exactly by 6?
11. 11.What is the smallest number you must add to 698 so that it divides exactly by 11?
12. 12.How many factors does 33 have?
13. 13.Which of these numbers divides exactly by 6? (a) 2073 (b) 2600 (c) 7858 (d) 4326
14. 14.Which of these numbers divides exactly by 4? (a) 7770 (b) 7197 (c) 9368 (d) 3301
15. 15.What is the smallest number you must add to 861 so that it divides exactly by 11?
16. 16.How many factors does 66 have?
17. 17.What is the smallest number you must add to 483 so that it divides exactly by 8?
18. 18.How many factors does 68 have?
19. 19.What is the smallest number you must take away from 890 so that it divides exactly by 11?
20. 20.What is the smallest number you must add to 319 so that it divides exactly by 13?
21. 21.Which of these numbers divides exactly by 9? (a) 5500 (b) 8578 (c) 7077 (d) 4518
22. 22.How many factors does 99 have?
23. 23.What is the smallest number you must add to 869 so that it divides exactly by 3?
24. 24.What is the smallest number you must take away from 530 so that it divides exactly by 12?
25. 25.What is the smallest number you must add to 599 so that it divides exactly by 9?
26. 26.What is the smallest number you must take away from 342 so that it divides exactly by 7?
27. 27.How many factors does 94 have?
28. 28.How many factors does 80 have?
29. 29.How many factors does 51 have?
30. 30.What is the smallest number you must take away from 713 so that it divides exactly by 7?
31. 31.What is the smallest number you must add to 205 so that it divides exactly by 13?
32. 32.Which of these numbers divides exactly by 9? (a) 8088 (b) 1278 (c) 3100 (d) 1751
33. 33.Which of these numbers divides exactly by 11? (a) 4364 (b) 5434 (c) 4882 (d) 4687
34. 34.What is the smallest number you must take away from 327 so that it divides exactly by 7?
35. 35.What is the smallest number you must add to 124 so that it divides exactly by 12?
36. 36.What is the smallest number you must take away from 562 so that it divides exactly by 4?
37. 37.Which of these numbers divides exactly by 4? (a) 2774 (b) 6648 (c) 6685 (d) 6793
38. 38.What is the smallest number you must add to 397 so that it divides exactly by 12?
39. 39.How many factors does 31 have?
40. 40.Which of these numbers divides exactly by 4? (a) 1790 (b) 1318 (c) 4953 (d) 8796

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