Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 316 · 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 33 have?
2. 2.What is the smallest number you must add to 326 so that it divides exactly by 4?
3. 3.What is the smallest number you must take away from 300 so that it divides exactly by 11?
4. 4.What is the smallest number you must add to 849 so that it divides exactly by 8?
5. 5.What is the smallest number you must add to 972 so that it divides exactly by 7?
6. 6.What is the smallest number you must add to 619 so that it divides exactly by 9?
7. 7.How many factors does 86 have?
8. 8.What is the smallest number you must take away from 201 so that it divides exactly by 4?
9. 9.What is the smallest number you must add to 516 so that it divides exactly by 8?
10. 10.Which of these numbers divides exactly by 6? (a) 2203 (b) 1923 (c) 1585 (d) 9036
11. 11.What is the smallest number you must add to 788 so that it divides exactly by 9?
12. 12.Which of these numbers divides exactly by 3? (a) 5706 (b) 7075 (c) 1550 (d) 2942
13. 13.How many factors does 17 have?
14. 14.What is the smallest number you must take away from 511 so that it divides exactly by 4?
15. 15.What is the smallest number you must take away from 685 so that it divides exactly by 4?
16. 16.Which of these numbers divides exactly by 9? (a) 5922 (b) 1996 (c) 5914 (d) 1130
17. 17.How many factors does 83 have?
18. 18.What is the smallest number you must add to 893 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 175 so that it divides exactly by 6?
20. 20.What is the smallest number you must take away from 525 so that it divides exactly by 4?
21. 21.Which of these numbers divides exactly by 6? (a) 8812 (b) 2859 (c) 3612 (d) 9802
22. 22.What is the smallest number you must add to 131 so that it divides exactly by 4?
23. 23.What is the smallest number you must add to 394 so that it divides exactly by 11?
24. 24.How many factors does 80 have?
25. 25.What is the smallest number you must take away from 805 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 446 so that it divides exactly by 9?
27. 27.Which of these numbers divides exactly by 3? (a) 5293 (b) 8903 (c) 3943 (d) 6708
28. 28.What is the smallest number you must add to 275 so that it divides exactly by 7?
29. 29.What is the smallest number you must take away from 349 so that it divides exactly by 9?
30. 30.What is the smallest number you must take away from 586 so that it divides exactly by 6?
31. 31.How many factors does 100 have?
32. 32.How many factors does 37 have?
33. 33.Which of these numbers divides exactly by 6? (a) 4073 (b) 4491 (c) 1302 (d) 2059
34. 34.What is the smallest number you must take away from 890 so that it divides exactly by 11?
35. 35.What is the smallest number you must add to 415 so that it divides exactly by 8?
36. 36.How many factors does 74 have?
37. 37.Which of these numbers divides exactly by 11? (a) 7479 (b) 7025 (c) 6993 (d) 3058
38. 38.What is the smallest number you must take away from 289 so that it divides exactly by 7?
39. 39.How many factors does 53 have?
40. 40.What is the smallest number you must add to 912 so that it divides exactly by 7?

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