Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 4 · 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 68 have?
2. 2.Which of these numbers divides exactly by 11? (a) 4620 (b) 4948 (c) 4757 (d) 8224
3. 3.What is the smallest number you must add to 787 so that it divides exactly by 8?
4. 4.Which of these numbers divides exactly by 6? (a) 3158 (b) 4324 (c) 7440 (d) 9460
5. 5.How many factors does 98 have?
6. 6.What is the smallest number you must add to 445 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 3? (a) 7774 (b) 9012 (c) 4952 (d) 8141
8. 8.What is the smallest number you must take away from 491 so that it divides exactly by 4?
9. 9.What is the smallest number you must take away from 852 so that it divides exactly by 7?
10. 10.What is the smallest number you must take away from 855 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 207 so that it divides exactly by 4?
12. 12.How many factors does 89 have?
13. 13.What is the smallest number you must take away from 339 so that it divides exactly by 6?
14. 14.What is the smallest number you must add to 304 so that it divides exactly by 3?
15. 15.What is the smallest number you must add to 170 so that it divides exactly by 7?
16. 16.What is the smallest number you must add to 421 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 8? (a) 5192 (b) 7898 (c) 7431 (d) 9076
18. 18.Which of these numbers divides exactly by 6? (a) 4247 (b) 9209 (c) 9117 (d) 7386
19. 19.Which of these numbers divides exactly by 3? (a) 2594 (b) 8101 (c) 7614 (d) 3215
20. 20.How many factors does 79 have?
21. 21.What is the smallest number you must add to 321 so that it divides exactly by 7?
22. 22.How many factors does 49 have?
23. 23.What is the smallest number you must add to 358 so that it divides exactly by 12?
24. 24.What is the smallest number you must add to 781 so that it divides exactly by 13?
25. 25.What is the smallest number you must take away from 976 so that it divides exactly by 12?
26. 26.What is the smallest number you must take away from 634 so that it divides exactly by 13?
27. 27.What is the smallest number you must take away from 235 so that it divides exactly by 12?
28. 28.Which of these numbers divides exactly by 3? (a) 2435 (b) 2927 (c) 2361 (d) 8177
29. 29.What is the smallest number you must add to 795 so that it divides exactly by 8?
30. 30.What is the smallest number you must take away from 962 so that it divides exactly by 9?
31. 31.What is the smallest number you must add to 630 so that it divides exactly by 13?
32. 32.How many factors does 47 have?
33. 33.How many factors does 86 have?
34. 34.What is the smallest number you must take away from 243 so that it divides exactly by 4?
35. 35.How many factors does 26 have?
36. 36.How many factors does 58 have?
37. 37.Which of these numbers divides exactly by 8? (a) 7736 (b) 9219 (c) 3267 (d) 3889
38. 38.How many factors does 17 have?
39. 39.What is the smallest number you must add to 714 so that it divides exactly by 9?
40. 40.What is the smallest number you must add to 468 so that it divides exactly by 7?

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