Question
Find Greatest Common Divisor of 6120 and 2040, using repeated division.
Answer
The GCD of given numbers is 2040.
Explanation
Step 1 : Place the numbers inside division bar:.
| 6120 | 2040 |
Step 2 : Divide numbers by 2.
| 2 | 6120 | 2040 |
| 3060 | 1020 |
Step 3 : Divide numbers by 2.
| 2 | 6120 | 2040 |
| 2 | 3060 | 1020 |
| 1530 | 510 |
Step 4 : Divide numbers by 2.
| 2 | 6120 | 2040 |
| 2 | 3060 | 1020 |
| 2 | 1530 | 510 |
| 765 | 255 |
Step 5 : Divide numbers by 3.
| 2 | 6120 | 2040 |
| 2 | 3060 | 1020 |
| 2 | 1530 | 510 |
| 3 | 765 | 255 |
| 255 | 85 |
Step 6 : Divide numbers by 5.
| 2 | 6120 | 2040 |
| 2 | 3060 | 1020 |
| 2 | 1530 | 510 |
| 3 | 765 | 255 |
| 5 | 255 | 85 |
| 51 | 17 |
Step 7 : Divide numbers by 17.
| 2 | 6120 | 2040 |
| 2 | 3060 | 1020 |
| 2 | 1530 | 510 |
| 3 | 765 | 255 |
| 5 | 255 | 85 |
| 17 | 51 | 17 |
| 3 | 1 |
Step 8 : Number 3 and 1, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot3\cdot5\cdot17 = 2040 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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