Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 158 · 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.Which of these numbers divides exactly by 9? (a) 9313 (b) 4777 (c) 9738 (d) 3469
2. 2.What is the smallest number you must take away from 969 so that it divides exactly by 13?
3. 3.How many factors does 58 have?
4. 4.Which of these numbers divides exactly by 9? (a) 5741 (b) 1838 (c) 7978 (d) 3528
5. 5.Which of these numbers divides exactly by 6? (a) 1114 (b) 3842 (c) 4255 (d) 1248
6. 6.How many factors does 28 have?
7. 7.What is the smallest number you must take away from 803 so that it divides exactly by 8?
8. 8.What is the smallest number you must take away from 202 so that it divides exactly by 6?
9. 9.What is the smallest number you must add to 169 so that it divides exactly by 3?
10. 10.What is the smallest number you must add to 371 so that it divides exactly by 3?
11. 11.What is the smallest number you must take away from 145 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 9? (a) 3256 (b) 7924 (c) 9787 (d) 9315
13. 13.What is the smallest number you must add to 341 so that it divides exactly by 12?
14. 14.How many factors does 35 have?
15. 15.What is the smallest number you must add to 797 so that it divides exactly by 7?
16. 16.How many factors does 37 have?
17. 17.Which of these numbers divides exactly by 3? (a) 7307 (b) 1998 (c) 1787 (d) 7327
18. 18.How many factors does 85 have?
19. 19.What is the smallest number you must add to 545 so that it divides exactly by 4?
20. 20.How many factors does 27 have?
21. 21.Which of these numbers divides exactly by 9? (a) 8649 (b) 8360 (c) 3619 (d) 9406
22. 22.What is the smallest number you must take away from 710 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 401 so that it divides exactly by 13?
24. 24.What is the smallest number you must take away from 196 so that it divides exactly by 12?
25. 25.What is the smallest number you must take away from 166 so that it divides exactly by 11?
26. 26.Which of these numbers divides exactly by 9? (a) 6471 (b) 9457 (c) 1364 (d) 7102
27. 27.What is the smallest number you must take away from 327 so that it divides exactly by 11?
28. 28.What is the smallest number you must add to 211 so that it divides exactly by 3?
29. 29.What is the smallest number you must take away from 321 so that it divides exactly by 11?
30. 30.How many factors does 71 have?
31. 31.What is the smallest number you must take away from 341 so that it divides exactly by 9?
32. 32.What is the smallest number you must add to 885 so that it divides exactly by 12?
33. 33.What is the smallest number you must add to 539 so that it divides exactly by 3?
34. 34.What is the smallest number you must take away from 410 so that it divides exactly by 13?
35. 35.Which of these numbers divides exactly by 6? (a) 4522 (b) 6182 (c) 1779 (d) 2844
36. 36.What is the smallest number you must take away from 159 so that it divides exactly by 9?
37. 37.Which of these numbers divides exactly by 6? (a) 3691 (b) 1915 (c) 6224 (d) 5892
38. 38.How many factors does 63 have?
39. 39.Which of these numbers divides exactly by 11? (a) 6710 (b) 6624 (c) 8334 (d) 3690
40. 40.Which of these numbers divides exactly by 9? (a) 9805 (b) 7404 (c) 6938 (d) 3600

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