Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 80 · 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 119 so that it divides exactly by 4?
2. 2.Which of these numbers divides exactly by 8? (a) 2460 (b) 2038 (c) 1096 (d) 1955
3. 3.What is the smallest number you must take away from 367 so that it divides exactly by 3?
4. 4.How many factors does 43 have?
5. 5.Which of these numbers divides exactly by 8? (a) 8076 (b) 7582 (c) 6496 (d) 3391
6. 6.What is the smallest number you must add to 865 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 6? (a) 4594 (b) 9197 (c) 1599 (d) 1194
8. 8.Which of these numbers divides exactly by 9? (a) 2441 (b) 2745 (c) 8536 (d) 8420
9. 9.What is the smallest number you must take away from 845 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 114 so that it divides exactly by 13?
11. 11.How many factors does 13 have?
12. 12.Which of these numbers divides exactly by 6? (a) 6001 (b) 4897 (c) 2498 (d) 5850
13. 13.What is the smallest number you must add to 652 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 825 so that it divides exactly by 7?
15. 15.What is the smallest number you must add to 702 so that it divides exactly by 4?
16. 16.How many factors does 26 have?
17. 17.How many factors does 12 have?
18. 18.How many factors does 65 have?
19. 19.How many factors does 25 have?
20. 20.Which of these numbers divides exactly by 8? (a) 2793 (b) 7847 (c) 2620 (d) 5632
21. 21.What is the smallest number you must add to 233 so that it divides exactly by 8?
22. 22.What is the smallest number you must add to 427 so that it divides exactly by 6?
23. 23.How many factors does 54 have?
24. 24.What is the smallest number you must add to 910 so that it divides exactly by 12?
25. 25.What is the smallest number you must add to 275 so that it divides exactly by 3?
26. 26.What is the smallest number you must take away from 955 so that it divides exactly by 13?
27. 27.Which of these numbers divides exactly by 3? (a) 3734 (b) 5798 (c) 8843 (d) 7428
28. 28.What is the smallest number you must add to 140 so that it divides exactly by 9?
29. 29.What is the smallest number you must add to 375 so that it divides exactly by 11?
30. 30.How many factors does 80 have?
31. 31.Which of these numbers divides exactly by 6? (a) 4824 (b) 9553 (c) 3519 (d) 4927
32. 32.What is the smallest number you must take away from 690 so that it divides exactly by 8?
33. 33.What is the smallest number you must add to 919 so that it divides exactly by 4?
34. 34.Which of these numbers divides exactly by 9? (a) 8718 (b) 1847 (c) 3207 (d) 1863
35. 35.What is the smallest number you must take away from 184 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 11? (a) 8166 (b) 5033 (c) 6706 (d) 1826
37. 37.What is the smallest number you must add to 183 so that it divides exactly by 13?
38. 38.How many factors does 91 have?
39. 39.What is the smallest number you must add to 525 so that it divides exactly by 13?
40. 40.How many factors does 88 have?

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