Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 3 · 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 43 have?
2. 2.What is the smallest number you must take away from 119 so that it divides exactly by 6?
3. 3.What is the smallest number you must add to 429 so that it divides exactly by 7?
4. 4.How many factors does 91 have?
5. 5.Which of these numbers divides exactly by 3? (a) 3499 (b) 1112 (c) 5807 (d) 9627
6. 6.Which of these numbers divides exactly by 9? (a) 4045 (b) 2989 (c) 6716 (d) 1098
7. 7.What is the smallest number you must add to 638 so that it divides exactly by 4?
8. 8.Which of these numbers divides exactly by 8? (a) 9278 (b) 7368 (c) 9797 (d) 3230
9. 9.Which of these numbers divides exactly by 8? (a) 8544 (b) 4698 (c) 2530 (d) 1970
10. 10.How many factors does 73 have?
11. 11.How many factors does 41 have?
12. 12.How many factors does 99 have?
13. 13.Which of these numbers divides exactly by 6? (a) 1890 (b) 3326 (c) 7229 (d) 4265
14. 14.Which of these numbers divides exactly by 9? (a) 7322 (b) 5582 (c) 9963 (d) 5397
15. 15.How many factors does 40 have?
16. 16.How many factors does 22 have?
17. 17.What is the smallest number you must add to 203 so that it divides exactly by 4?
18. 18.Which of these numbers divides exactly by 3? (a) 2097 (b) 9037 (c) 6923 (d) 2122
19. 19.What is the smallest number you must add to 234 so that it divides exactly by 12?
20. 20.How many factors does 53 have?
21. 21.How many factors does 77 have?
22. 22.What is the smallest number you must add to 407 so that it divides exactly by 12?
23. 23.What is the smallest number you must add to 633 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 517 so that it divides exactly by 12?
25. 25.How many factors does 54 have?
26. 26.Which of these numbers divides exactly by 11? (a) 8926 (b) 6919 (c) 3647 (d) 1818
27. 27.What is the smallest number you must take away from 219 so that it divides exactly by 9?
28. 28.What is the smallest number you must take away from 563 so that it divides exactly by 6?
29. 29.Which of these numbers divides exactly by 9? (a) 9384 (b) 8639 (c) 1113 (d) 6921
30. 30.What is the smallest number you must take away from 627 so that it divides exactly by 6?
31. 31.What is the smallest number you must add to 941 so that it divides exactly by 6?
32. 32.Which of these numbers divides exactly by 6? (a) 1866 (b) 3793 (c) 6385 (d) 7513
33. 33.What is the smallest number you must take away from 189 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 154 so that it divides exactly by 6?
35. 35.What is the smallest number you must take away from 663 so that it divides exactly by 9?
36. 36.What is the smallest number you must take away from 968 so that it divides exactly by 13?
37. 37.How many factors does 76 have?
38. 38.What is the smallest number you must add to 426 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 483 so that it divides exactly by 11?
40. 40.How many factors does 18 have?

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