Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 266 · 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 88 have?
2. 2.Which of these numbers divides exactly by 11? (a) 4832 (b) 4454 (c) 3082 (d) 7986
3. 3.What is the smallest number you must add to 647 so that it divides exactly by 4?
4. 4.What is the smallest number you must take away from 544 so that it divides exactly by 13?
5. 5.How many factors does 59 have?
6. 6.Which of these numbers divides exactly by 9? (a) 9819 (b) 3766 (c) 2909 (d) 2725
7. 7.What is the smallest number you must take away from 829 so that it divides exactly by 3?
8. 8.How many factors does 81 have?
9. 9.How many factors does 43 have?
10. 10.How many factors does 26 have?
11. 11.What is the smallest number you must add to 658 so that it divides exactly by 9?
12. 12.What is the smallest number you must add to 540 so that it divides exactly by 8?
13. 13.What is the smallest number you must add to 390 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 164 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 979 so that it divides exactly by 8?
16. 16.What is the smallest number you must take away from 362 so that it divides exactly by 11?
17. 17.Which of these numbers divides exactly by 6? (a) 4299 (b) 9268 (c) 2301 (d) 2160
18. 18.How many factors does 47 have?
19. 19.What is the smallest number you must take away from 222 so that it divides exactly by 7?
20. 20.Which of these numbers divides exactly by 6? (a) 9742 (b) 9469 (c) 4482 (d) 1081
21. 21.What is the smallest number you must add to 793 so that it divides exactly by 4?
22. 22.Which of these numbers divides exactly by 6? (a) 4950 (b) 2721 (c) 8199 (d) 7331
23. 23.Which of these numbers divides exactly by 8? (a) 3232 (b) 4393 (c) 9206 (d) 1431
24. 24.Which of these numbers divides exactly by 8? (a) 9730 (b) 1757 (c) 4178 (d) 1096
25. 25.Which of these numbers divides exactly by 4? (a) 5825 (b) 4297 (c) 5732 (d) 2134
26. 26.How many factors does 57 have?
27. 27.What is the smallest number you must add to 677 so that it divides exactly by 11?
28. 28.Which of these numbers divides exactly by 9? (a) 8492 (b) 9013 (c) 6453 (d) 4357
29. 29.What is the smallest number you must take away from 142 so that it divides exactly by 7?
30. 30.What is the smallest number you must take away from 710 so that it divides exactly by 3?
31. 31.What is the smallest number you must add to 122 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 123 so that it divides exactly by 9?
33. 33.What is the smallest number you must add to 120 so that it divides exactly by 7?
34. 34.How many factors does 32 have?
35. 35.What is the smallest number you must add to 805 so that it divides exactly by 13?
36. 36.Which of these numbers divides exactly by 3? (a) 7639 (b) 3496 (c) 9108 (d) 6653
37. 37.What is the smallest number you must take away from 789 so that it divides exactly by 13?
38. 38.How many factors does 65 have?
39. 39.Which of these numbers divides exactly by 6? (a) 5793 (b) 6929 (c) 6425 (d) 7140
40. 40.What is the smallest number you must take away from 134 so that it divides exactly by 7?

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