Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 128 · 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.Which of these numbers divides exactly by 8? (a) 5847 (b) 1184 (c) 9355 (d) 5795
2. 2.What is the smallest number you must add to 930 so that it divides exactly by 9?
3. 3.Which of these numbers divides exactly by 11? (a) 7264 (b) 5128 (c) 3707 (d) 8346
4. 4.Which of these numbers divides exactly by 4? (a) 9946 (b) 4213 (c) 2626 (d) 9608
5. 5.How many factors does 67 have?
6. 6.What is the smallest number you must add to 443 so that it divides exactly by 8?
7. 7.What is the smallest number you must take away from 117 so that it divides exactly by 12?
8. 8.What is the smallest number you must add to 941 so that it divides exactly by 4?
9. 9.How many factors does 39 have?
10. 10.What is the smallest number you must take away from 662 so that it divides exactly by 6?
11. 11.How many factors does 47 have?
12. 12.How many factors does 90 have?
13. 13.Which of these numbers divides exactly by 4? (a) 6274 (b) 3178 (c) 2135 (d) 1224
14. 14.What is the smallest number you must take away from 656 so that it divides exactly by 11?
15. 15.How many factors does 79 have?
16. 16.What is the smallest number you must take away from 591 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 4? (a) 6489 (b) 8136 (c) 7170 (d) 7479
18. 18.What is the smallest number you must take away from 951 so that it divides exactly by 7?
19. 19.How many factors does 29 have?
20. 20.What is the smallest number you must add to 546 so that it divides exactly by 4?
21. 21.Which of these numbers divides exactly by 9? (a) 6835 (b) 1268 (c) 1455 (d) 9252
22. 22.Which of these numbers divides exactly by 3? (a) 7688 (b) 7687 (c) 6815 (d) 7023
23. 23.What is the smallest number you must add to 535 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 3? (a) 9977 (b) 6483 (c) 1801 (d) 9269
25. 25.Which of these numbers divides exactly by 11? (a) 6853 (b) 9432 (c) 7643 (d) 5960
26. 26.How many factors does 100 have?
27. 27.What is the smallest number you must take away from 781 so that it divides exactly by 6?
28. 28.How many factors does 23 have?
29. 29.What is the smallest number you must add to 438 so that it divides exactly by 12?
30. 30.What is the smallest number you must take away from 785 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 9? (a) 9946 (b) 1716 (c) 7263 (d) 8093
32. 32.What is the smallest number you must add to 312 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 4? (a) 6980 (b) 2657 (c) 9935 (d) 7573
34. 34.Which of these numbers divides exactly by 4? (a) 4158 (b) 6976 (c) 3053 (d) 1265
35. 35.Which of these numbers divides exactly by 6? (a) 7662 (b) 6485 (c) 3307 (d) 9429
36. 36.What is the smallest number you must take away from 415 so that it divides exactly by 13?
37. 37.What is the smallest number you must add to 692 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 278 so that it divides exactly by 4?
39. 39.What is the smallest number you must take away from 939 so that it divides exactly by 7?
40. 40.What is the smallest number you must add to 964 so that it divides exactly by 9?

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