Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 83 · 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 276 so that it divides exactly by 9?
2. 2.What is the smallest number you must take away from 155 so that it divides exactly by 11?
3. 3.What is the smallest number you must add to 317 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 6? (a) 6483 (b) 2384 (c) 4198 (d) 9996
5. 5.What is the smallest number you must take away from 905 so that it divides exactly by 6?
6. 6.What is the smallest number you must take away from 205 so that it divides exactly by 4?
7. 7.How many factors does 62 have?
8. 8.How many factors does 52 have?
9. 9.How many factors does 70 have?
10. 10.How many factors does 16 have?
11. 11.What is the smallest number you must add to 310 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 681 so that it divides exactly by 8?
13. 13.Which of these numbers divides exactly by 3? (a) 5660 (b) 1261 (c) 2562 (d) 1982
14. 14.Which of these numbers divides exactly by 11? (a) 1661 (b) 3154 (c) 1532 (d) 5402
15. 15.What is the smallest number you must add to 717 so that it divides exactly by 11?
16. 16.How many factors does 47 have?
17. 17.Which of these numbers divides exactly by 9? (a) 4994 (b) 7777 (c) 2054 (d) 1773
18. 18.What is the smallest number you must take away from 129 so that it divides exactly by 12?
19. 19.Which of these numbers divides exactly by 8? (a) 3879 (b) 8092 (c) 1892 (d) 5080
20. 20.What is the smallest number you must add to 963 so that it divides exactly by 7?
21. 21.How many factors does 39 have?
22. 22.What is the smallest number you must take away from 238 so that it divides exactly by 6?
23. 23.What is the smallest number you must add to 255 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 541 so that it divides exactly by 6?
25. 25.Which of these numbers divides exactly by 9? (a) 6957 (b) 2717 (c) 3703 (d) 7286
26. 26.How many factors does 33 have?
27. 27.What is the smallest number you must add to 321 so that it divides exactly by 7?
28. 28.How many factors does 51 have?
29. 29.How many factors does 36 have?
30. 30.What is the smallest number you must add to 223 so that it divides exactly by 6?
31. 31.How many factors does 13 have?
32. 32.How many factors does 34 have?
33. 33.Which of these numbers divides exactly by 3? (a) 3551 (b) 6859 (c) 7154 (d) 1050
34. 34.What is the smallest number you must take away from 697 so that it divides exactly by 8?
35. 35.What is the smallest number you must add to 996 so that it divides exactly by 13?
36. 36.What is the smallest number you must add to 411 so that it divides exactly by 7?
37. 37.What is the smallest number you must add to 407 so that it divides exactly by 8?
38. 38.What is the smallest number you must add to 907 so that it divides exactly by 8?
39. 39.What is the smallest number you must take away from 229 so that it divides exactly by 3?
40. 40.How many factors does 17 have?

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