Question
Find Greatest Common Divisor of 800, 400 and 200, using repeated division.
Answer
The GCD of given numbers is 200.
Explanation
Step 1 : Place the numbers inside division bar:.
| 800 | 400 | 200 |
Step 2 : Divide numbers by 2.
| 2 | 800 | 400 | 200 |
| 400 | 200 | 100 |
Step 3 : Divide numbers by 2.
| 2 | 800 | 400 | 200 |
| 2 | 400 | 200 | 100 |
| 200 | 100 | 50 |
Step 4 : Divide numbers by 2.
| 2 | 800 | 400 | 200 |
| 2 | 400 | 200 | 100 |
| 2 | 200 | 100 | 50 |
| 100 | 50 | 25 |
Step 5 : Divide numbers by 5.
| 2 | 800 | 400 | 200 |
| 2 | 400 | 200 | 100 |
| 2 | 200 | 100 | 50 |
| 5 | 100 | 50 | 25 |
| 20 | 10 | 5 |
Step 6 : Divide numbers by 5.
| 2 | 800 | 400 | 200 |
| 2 | 400 | 200 | 100 |
| 2 | 200 | 100 | 50 |
| 5 | 100 | 50 | 25 |
| 5 | 20 | 10 | 5 |
| 4 | 2 | 1 |
Step 7 : Number 4, 2 and 1, cannot be divided any more. The GCD is:
This solution can be visualized using a Venn diagram.
0,0
800
400
200
2
2
2
5
5
2
2
The GCD equals the product of the numbers at the intersection.
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