Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 72 · 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 add to 391 so that it divides exactly by 6?
2. 2.How many factors does 56 have?
3. 3.What is the smallest number you must take away from 393 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 11? (a) 7831 (b) 5742 (c) 5776 (d) 6957
5. 5.How many factors does 14 have?
6. 6.What is the smallest number you must take away from 388 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 8? (a) 6126 (b) 8637 (c) 3354 (d) 4896
8. 8.What is the smallest number you must take away from 310 so that it divides exactly by 11?
9. 9.What is the smallest number you must take away from 163 so that it divides exactly by 4?
10. 10.What is the smallest number you must add to 568 so that it divides exactly by 6?
11. 11.What is the smallest number you must take away from 616 so that it divides exactly by 12?
12. 12.What is the smallest number you must take away from 193 so that it divides exactly by 3?
13. 13.How many factors does 54 have?
14. 14.Which of these numbers divides exactly by 9? (a) 4858 (b) 7791 (c) 2610 (d) 6436
15. 15.What is the smallest number you must take away from 752 so that it divides exactly by 9?
16. 16.How many factors does 31 have?
17. 17.What is the smallest number you must take away from 385 so that it divides exactly by 3?
18. 18.What is the smallest number you must take away from 163 so that it divides exactly by 3?
19. 19.What is the smallest number you must take away from 355 so that it divides exactly by 6?
20. 20.Which of these numbers divides exactly by 11? (a) 2940 (b) 2133 (c) 4948 (d) 8294
21. 21.How many factors does 89 have?
22. 22.What is the smallest number you must add to 303 so that it divides exactly by 4?
23. 23.How many factors does 65 have?
24. 24.Which of these numbers divides exactly by 3? (a) 2710 (b) 9685 (c) 8937 (d) 1753
25. 25.Which of these numbers divides exactly by 4? (a) 8440 (b) 7553 (c) 2985 (d) 1569
26. 26.What is the smallest number you must add to 987 so that it divides exactly by 8?
27. 27.How many factors does 19 have?
28. 28.How many factors does 92 have?
29. 29.Which of these numbers divides exactly by 9? (a) 8089 (b) 2430 (c) 8610 (d) 5568
30. 30.What is the smallest number you must take away from 262 so that it divides exactly by 7?
31. 31.What is the smallest number you must take away from 569 so that it divides exactly by 7?
32. 32.What is the smallest number you must take away from 346 so that it divides exactly by 4?
33. 33.How many factors does 100 have?
34. 34.What is the smallest number you must add to 730 so that it divides exactly by 3?
35. 35.What is the smallest number you must take away from 865 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 799 so that it divides exactly by 9?
37. 37.How many factors does 33 have?
38. 38.How many factors does 42 have?
39. 39.What is the smallest number you must take away from 631 so that it divides exactly by 13?
40. 40.What is the smallest number you must add to 525 so that it divides exactly by 8?

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