Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 31 · 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 add to 471 so that it divides exactly by 6?
2. 2.Which of these numbers divides exactly by 3? (a) 6778 (b) 2668 (c) 3153 (d) 1108
3. 3.Which of these numbers divides exactly by 6? (a) 3391 (b) 3295 (c) 4926 (d) 9572
4. 4.What is the smallest number you must take away from 221 so that it divides exactly by 9?
5. 5.What is the smallest number you must add to 646 so that it divides exactly by 13?
6. 6.What is the smallest number you must add to 490 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 3? (a) 3594 (b) 5524 (c) 9659 (d) 1483
8. 8.What is the smallest number you must take away from 323 so that it divides exactly by 12?
9. 9.Which of these numbers divides exactly by 9? (a) 6943 (b) 6305 (c) 6426 (d) 8023
10. 10.How many factors does 59 have?
11. 11.Which of these numbers divides exactly by 11? (a) 8149 (b) 3430 (c) 3964 (d) 9207
12. 12.Which of these numbers divides exactly by 8? (a) 5658 (b) 6226 (c) 4891 (d) 5808
13. 13.How many factors does 22 have?
14. 14.What is the smallest number you must take away from 217 so that it divides exactly by 12?
15. 15.How many factors does 45 have?
16. 16.What is the smallest number you must take away from 422 so that it divides exactly by 8?
17. 17.Which of these numbers divides exactly by 3? (a) 9188 (b) 8333 (c) 1097 (d) 3276
18. 18.How many factors does 29 have?
19. 19.What is the smallest number you must add to 187 so that it divides exactly by 3?
20. 20.How many factors does 30 have?
21. 21.Which of these numbers divides exactly by 11? (a) 6048 (b) 7193 (c) 4508 (d) 2112
22. 22.What is the smallest number you must add to 754 so that it divides exactly by 4?
23. 23.How many factors does 18 have?
24. 24.What is the smallest number you must add to 241 so that it divides exactly by 12?
25. 25.What is the smallest number you must take away from 417 so that it divides exactly by 6?
26. 26.What is the smallest number you must take away from 231 so that it divides exactly by 9?
27. 27.What is the smallest number you must add to 833 so that it divides exactly by 12?
28. 28.What is the smallest number you must take away from 783 so that it divides exactly by 6?
29. 29.How many factors does 24 have?
30. 30.What is the smallest number you must add to 390 so that it divides exactly by 4?
31. 31.What is the smallest number you must take away from 965 so that it divides exactly by 13?
32. 32.What is the smallest number you must add to 134 so that it divides exactly by 7?
33. 33.What is the smallest number you must add to 748 so that it divides exactly by 3?
34. 34.Which of these numbers divides exactly by 9? (a) 1332 (b) 2452 (c) 7275 (d) 6395
35. 35.What is the smallest number you must add to 347 so that it divides exactly by 4?
36. 36.How many factors does 57 have?
37. 37.Which of these numbers divides exactly by 4? (a) 3109 (b) 1556 (c) 9197 (d) 7615
38. 38.How many factors does 55 have?
39. 39.Which of these numbers divides exactly by 4? (a) 3027 (b) 1295 (c) 3560 (d) 3521
40. 40.What is the smallest number you must add to 450 so that it divides exactly by 13?

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