Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 285 · 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 549 so that it divides exactly by 6?
2. 2.What is the smallest number you must take away from 806 so that it divides exactly by 11?
3. 3.What is the smallest number you must take away from 577 so that it divides exactly by 13?
4. 4.What is the smallest number you must add to 341 so that it divides exactly by 9?
5. 5.What is the smallest number you must take away from 246 so that it divides exactly by 13?
6. 6.What is the smallest number you must add to 885 so that it divides exactly by 6?
7. 7.How many factors does 96 have?
8. 8.What is the smallest number you must take away from 536 so that it divides exactly by 11?
9. 9.What is the smallest number you must take away from 541 so that it divides exactly by 3?
10. 10.What is the smallest number you must add to 898 so that it divides exactly by 9?
11. 11.How many factors does 38 have?
12. 12.What is the smallest number you must take away from 797 so that it divides exactly by 6?
13. 13.Which of these numbers divides exactly by 9? (a) 8010 (b) 1039 (c) 8873 (d) 3013
14. 14.What is the smallest number you must add to 359 so that it divides exactly by 3?
15. 15.What is the smallest number you must take away from 172 so that it divides exactly by 6?
16. 16.What is the smallest number you must add to 655 so that it divides exactly by 3?
17. 17.What is the smallest number you must take away from 304 so that it divides exactly by 3?
18. 18.Which of these numbers divides exactly by 3? (a) 5899 (b) 9364 (c) 2641 (d) 5853
19. 19.How many factors does 75 have?
20. 20.What is the smallest number you must take away from 257 so that it divides exactly by 12?
21. 21.How many factors does 62 have?
22. 22.What is the smallest number you must add to 290 so that it divides exactly by 8?
23. 23.Which of these numbers divides exactly by 11? (a) 3019 (b) 9784 (c) 8140 (d) 9539
24. 24.What is the smallest number you must add to 159 so that it divides exactly by 7?
25. 25.What is the smallest number you must take away from 438 so that it divides exactly by 9?
26. 26.What is the smallest number you must take away from 135 so that it divides exactly by 7?
27. 27.How many factors does 50 have?
28. 28.Which of these numbers divides exactly by 6? (a) 8069 (b) 5197 (c) 3222 (d) 2011
29. 29.Which of these numbers divides exactly by 4? (a) 3330 (b) 2650 (c) 4796 (d) 5713
30. 30.Which of these numbers divides exactly by 11? (a) 7472 (b) 1995 (c) 5742 (d) 5861
31. 31.How many factors does 72 have?
32. 32.What is the smallest number you must add to 734 so that it divides exactly by 6?
33. 33.Which of these numbers divides exactly by 6? (a) 9219 (b) 8559 (c) 3890 (d) 4716
34. 34.What is the smallest number you must take away from 719 so that it divides exactly by 13?
35. 35.What is the smallest number you must take away from 317 so that it divides exactly by 3?
36. 36.What is the smallest number you must add to 169 so that it divides exactly by 3?
37. 37.What is the smallest number you must take away from 210 so that it divides exactly by 8?
38. 38.What is the smallest number you must take away from 619 so that it divides exactly by 13?
39. 39.Which of these numbers divides exactly by 4? (a) 1030 (b) 4328 (c) 6985 (d) 7631
40. 40.What is the smallest number you must take away from 700 so that it divides exactly by 11?

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