Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 204 · 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 781 so that it divides exactly by 4?
2. 2.What is the smallest number you must take away from 775 so that it divides exactly by 8?
3. 3.How many factors does 95 have?
4. 4.What is the smallest number you must add to 169 so that it divides exactly by 11?
5. 5.Which of these numbers divides exactly by 9? (a) 5763 (b) 3005 (c) 3512 (d) 7929
6. 6.What is the smallest number you must take away from 801 so that it divides exactly by 12?
7. 7.What is the smallest number you must add to 285 so that it divides exactly by 8?
8. 8.How many factors does 94 have?
9. 9.What is the smallest number you must take away from 600 so that it divides exactly by 13?
10. 10.Which of these numbers divides exactly by 4? (a) 3234 (b) 5291 (c) 9899 (d) 1760
11. 11.How many factors does 41 have?
12. 12.What is the smallest number you must add to 788 so that it divides exactly by 11?
13. 13.What is the smallest number you must add to 332 so that it divides exactly by 12?
14. 14.Which of these numbers divides exactly by 8? (a) 6352 (b) 8370 (c) 2826 (d) 1111
15. 15.What is the smallest number you must add to 985 so that it divides exactly by 4?
16. 16.What is the smallest number you must take away from 339 so that it divides exactly by 12?
17. 17.What is the smallest number you must add to 938 so that it divides exactly by 3?
18. 18.How many factors does 23 have?
19. 19.What is the smallest number you must take away from 276 so that it divides exactly by 8?
20. 20.What is the smallest number you must add to 775 so that it divides exactly by 9?
21. 21.Which of these numbers divides exactly by 4? (a) 8318 (b) 3206 (c) 7968 (d) 7958
22. 22.What is the smallest number you must add to 665 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 694 so that it divides exactly by 13?
24. 24.Which of these numbers divides exactly by 11? (a) 6802 (b) 6072 (c) 9522 (d) 6832
25. 25.What is the smallest number you must add to 431 so that it divides exactly by 8?
26. 26.What is the smallest number you must add to 718 so that it divides exactly by 4?
27. 27.Which of these numbers divides exactly by 6? (a) 2397 (b) 1260 (c) 7895 (d) 3955
28. 28.What is the smallest number you must take away from 824 so that it divides exactly by 13?
29. 29.What is the smallest number you must add to 388 so that it divides exactly by 8?
30. 30.What is the smallest number you must take away from 137 so that it divides exactly by 11?
31. 31.What is the smallest number you must add to 362 so that it divides exactly by 12?
32. 32.What is the smallest number you must add to 790 so that it divides exactly by 3?
33. 33.Which of these numbers divides exactly by 6? (a) 6722 (b) 8568 (c) 1355 (d) 7864
34. 34.How many factors does 72 have?
35. 35.Which of these numbers divides exactly by 3? (a) 9345 (b) 6878 (c) 6007 (d) 7786
36. 36.Which of these numbers divides exactly by 3? (a) 9247 (b) 3591 (c) 8966 (d) 6562
37. 37.How many factors does 34 have?
38. 38.How many factors does 22 have?
39. 39.What is the smallest number you must take away from 527 so that it divides exactly by 7?
40. 40.How many factors does 44 have?

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