Question
Find Greatest Common Divisor of 200, 1000 and 3000, using repeated division.
Answer
The GCD of given numbers is 200.
Explanation
Step 1 : Place the numbers inside division bar:.
| 200 | 1000 | 3000 |
Step 2 : Divide numbers by 2.
| 2 | 200 | 1000 | 3000 |
| 100 | 500 | 1500 |
Step 3 : Divide numbers by 2.
| 2 | 200 | 1000 | 3000 |
| 2 | 100 | 500 | 1500 |
| 50 | 250 | 750 |
Step 4 : Divide numbers by 2.
| 2 | 200 | 1000 | 3000 |
| 2 | 100 | 500 | 1500 |
| 2 | 50 | 250 | 750 |
| 25 | 125 | 375 |
Step 5 : Divide numbers by 5.
| 2 | 200 | 1000 | 3000 |
| 2 | 100 | 500 | 1500 |
| 2 | 50 | 250 | 750 |
| 5 | 25 | 125 | 375 |
| 5 | 25 | 75 |
Step 6 : Divide numbers by 5.
| 2 | 200 | 1000 | 3000 |
| 2 | 100 | 500 | 1500 |
| 2 | 50 | 250 | 750 |
| 5 | 25 | 125 | 375 |
| 5 | 5 | 25 | 75 |
| 1 | 5 | 15 |
Step 7 : Number 1, 5 and 15, cannot be divided any more. The GCD is:
This solution can be visualized using a Venn diagram.
0,0
200
1000
3000
2
2
2
5
5
5
3
The GCD equals the product of the numbers at the intersection.
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