Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 138 · 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 11? (a) 4154 (b) 2162 (c) 1738 (d) 8957
2. 2.What is the smallest number you must add to 780 so that it divides exactly by 11?
3. 3.Which of these numbers divides exactly by 6? (a) 6834 (b) 1705 (c) 9392 (d) 7082
4. 4.Which of these numbers divides exactly by 8? (a) 1062 (b) 7059 (c) 9190 (d) 3320
5. 5.Which of these numbers divides exactly by 9? (a) 4140 (b) 1928 (c) 6761 (d) 2838
6. 6.Which of these numbers divides exactly by 8? (a) 5778 (b) 6060 (c) 5240 (d) 9647
7. 7.Which of these numbers divides exactly by 3? (a) 4449 (b) 1945 (c) 7903 (d) 7655
8. 8.How many factors does 98 have?
9. 9.What is the smallest number you must add to 401 so that it divides exactly by 8?
10. 10.How many factors does 66 have?
11. 11.What is the smallest number you must add to 265 so that it divides exactly by 11?
12. 12.Which of these numbers divides exactly by 6? (a) 7636 (b) 4674 (c) 1387 (d) 7955
13. 13.Which of these numbers divides exactly by 6? (a) 6342 (b) 2032 (c) 5425 (d) 4803
14. 14.What is the smallest number you must add to 798 so that it divides exactly by 11?
15. 15.Which of these numbers divides exactly by 3? (a) 2597 (b) 2681 (c) 4838 (d) 5865
16. 16.What is the smallest number you must add to 218 so that it divides exactly by 12?
17. 17.What is the smallest number you must take away from 811 so that it divides exactly by 7?
18. 18.Which of these numbers divides exactly by 8? (a) 4389 (b) 1017 (c) 1680 (d) 2577
19. 19.Which of these numbers divides exactly by 11? (a) 1023 (b) 7206 (c) 4044 (d) 7504
20. 20.How many factors does 93 have?
21. 21.What is the smallest number you must take away from 989 so that it divides exactly by 9?
22. 22.Which of these numbers divides exactly by 6? (a) 5991 (b) 2991 (c) 8136 (d) 8456
23. 23.What is the smallest number you must take away from 714 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 338 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 138 so that it divides exactly by 7?
26. 26.How many factors does 85 have?
27. 27.Which of these numbers divides exactly by 8? (a) 3826 (b) 3034 (c) 1565 (d) 4072
28. 28.What is the smallest number you must add to 688 so that it divides exactly by 13?
29. 29.How many factors does 36 have?
30. 30.What is the smallest number you must take away from 639 so that it divides exactly by 8?
31. 31.How many factors does 37 have?
32. 32.What is the smallest number you must take away from 589 so that it divides exactly by 7?
33. 33.What is the smallest number you must take away from 284 so that it divides exactly by 12?
34. 34.What is the smallest number you must take away from 922 so that it divides exactly by 12?
35. 35.What is the smallest number you must take away from 485 so that it divides exactly by 4?
36. 36.How many factors does 70 have?
37. 37.How many factors does 59 have?
38. 38.Which of these numbers divides exactly by 4? (a) 5950 (b) 1280 (c) 1565 (d) 9747
39. 39.What is the smallest number you must add to 295 so that it divides exactly by 7?
40. 40.What is the smallest number you must take away from 949 so that it divides exactly by 11?

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