Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 209 · 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 4? (a) 8609 (b) 7146 (c) 8331 (d) 9572
2. 2.What is the smallest number you must take away from 344 so that it divides exactly by 9?
3. 3.What is the smallest number you must take away from 732 so that it divides exactly by 9?
4. 4.Which of these numbers divides exactly by 6? (a) 9340 (b) 8243 (c) 2340 (d) 1159
5. 5.What is the smallest number you must add to 406 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 501 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 9? (a) 9866 (b) 3231 (c) 4596 (d) 9742
8. 8.How many factors does 95 have?
9. 9.What is the smallest number you must take away from 805 so that it divides exactly by 9?
10. 10.What is the smallest number you must take away from 675 so that it divides exactly by 13?
11. 11.How many factors does 34 have?
12. 12.How many factors does 28 have?
13. 13.Which of these numbers divides exactly by 11? (a) 7711 (b) 8279 (c) 8891 (d) 3969
14. 14.Which of these numbers divides exactly by 6? (a) 1345 (b) 6263 (c) 5083 (d) 2430
15. 15.Which of these numbers divides exactly by 3? (a) 8020 (b) 5597 (c) 4194 (d) 4544
16. 16.Which of these numbers divides exactly by 3? (a) 8623 (b) 9629 (c) 9615 (d) 2272
17. 17.How many factors does 48 have?
18. 18.What is the smallest number you must take away from 522 so that it divides exactly by 11?
19. 19.What is the smallest number you must take away from 423 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 767 so that it divides exactly by 4?
21. 21.What is the smallest number you must take away from 352 so that it divides exactly by 3?
22. 22.Which of these numbers divides exactly by 9? (a) 8162 (b) 5165 (c) 7353 (d) 1348
23. 23.What is the smallest number you must add to 351 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 3? (a) 5905 (b) 7479 (c) 1330 (d) 5984
25. 25.What is the smallest number you must add to 510 so that it divides exactly by 8?
26. 26.What is the smallest number you must take away from 137 so that it divides exactly by 3?
27. 27.What is the smallest number you must add to 527 so that it divides exactly by 3?
28. 28.How many factors does 36 have?
29. 29.What is the smallest number you must add to 409 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 478 so that it divides exactly by 11?
31. 31.How many factors does 46 have?
32. 32.What is the smallest number you must add to 425 so that it divides exactly by 12?
33. 33.What is the smallest number you must take away from 892 so that it divides exactly by 12?
34. 34.How many factors does 86 have?
35. 35.What is the smallest number you must add to 805 so that it divides exactly by 12?
36. 36.What is the smallest number you must take away from 786 so that it divides exactly by 9?
37. 37.What is the smallest number you must take away from 791 so that it divides exactly by 3?
38. 38.How many factors does 64 have?
39. 39.Which of these numbers divides exactly by 9? (a) 4060 (b) 4711 (c) 1080 (d) 9125
40. 40.What is the smallest number you must take away from 752 so that it divides exactly by 12?

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