Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 252 · 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 524 so that it divides exactly by 6?
2. 2.What is the smallest number you must add to 544 so that it divides exactly by 7?
3. 3.What is the smallest number you must add to 841 so that it divides exactly by 6?
4. 4.How many factors does 93 have?
5. 5.How many factors does 31 have?
6. 6.How many factors does 66 have?
7. 7.How many factors does 12 have?
8. 8.How many factors does 51 have?
9. 9.Which of these numbers divides exactly by 3? (a) 4684 (b) 9339 (c) 6424 (d) 2965
10. 10.What is the smallest number you must take away from 690 so that it divides exactly by 11?
11. 11.What is the smallest number you must take away from 101 so that it divides exactly by 3?
12. 12.What is the smallest number you must take away from 373 so that it divides exactly by 8?
13. 13.How many factors does 19 have?
14. 14.How many factors does 50 have?
15. 15.What is the smallest number you must add to 407 so that it divides exactly by 6?
16. 16.How many factors does 20 have?
17. 17.Which of these numbers divides exactly by 9? (a) 9172 (b) 9405 (c) 4924 (d) 1516
18. 18.What is the smallest number you must add to 196 so that it divides exactly by 9?
19. 19.What is the smallest number you must add to 287 so that it divides exactly by 12?
20. 20.What is the smallest number you must add to 897 so that it divides exactly by 4?
21. 21.Which of these numbers divides exactly by 9? (a) 3370 (b) 8626 (c) 1809 (d) 7476
22. 22.What is the smallest number you must take away from 285 so that it divides exactly by 11?
23. 23.How many factors does 32 have?
24. 24.What is the smallest number you must add to 283 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 850 so that it divides exactly by 7?
26. 26.What is the smallest number you must add to 168 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 690 so that it divides exactly by 7?
28. 28.What is the smallest number you must add to 444 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 987 so that it divides exactly by 11?
30. 30.What is the smallest number you must add to 487 so that it divides exactly by 8?
31. 31.What is the smallest number you must take away from 149 so that it divides exactly by 3?
32. 32.What is the smallest number you must take away from 305 so that it divides exactly by 3?
33. 33.What is the smallest number you must add to 782 so that it divides exactly by 7?
34. 34.Which of these numbers divides exactly by 9? (a) 2533 (b) 9588 (c) 1962 (d) 6437
35. 35.What is the smallest number you must take away from 993 so that it divides exactly by 11?
36. 36.Which of these numbers divides exactly by 11? (a) 1738 (b) 9785 (c) 7663 (d) 1156
37. 37.What is the smallest number you must take away from 802 so that it divides exactly by 7?
38. 38.How many factors does 99 have?
39. 39.Which of these numbers divides exactly by 9? (a) 5928 (b) 6565 (c) 5582 (d) 4491
40. 40.How many factors does 68 have?

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