Question
Find Greatest Common Divisor of 2808, 1620 and 3132, using repeated division.
Answer
The GCD of given numbers is 108.
Explanation
Step 1 : Place the numbers inside division bar:.
| 2808 | 1620 | 3132 |
Step 2 : Divide numbers by 2.
| 2 | 2808 | 1620 | 3132 |
| 1404 | 810 | 1566 |
Step 3 : Divide numbers by 2.
| 2 | 2808 | 1620 | 3132 |
| 2 | 1404 | 810 | 1566 |
| 702 | 405 | 783 |
Step 4 : Divide numbers by 3.
| 2 | 2808 | 1620 | 3132 |
| 2 | 1404 | 810 | 1566 |
| 3 | 702 | 405 | 783 |
| 234 | 135 | 261 |
Step 5 : Divide numbers by 3.
| 2 | 2808 | 1620 | 3132 |
| 2 | 1404 | 810 | 1566 |
| 3 | 702 | 405 | 783 |
| 3 | 234 | 135 | 261 |
| 78 | 45 | 87 |
Step 6 : Divide numbers by 3.
| 2 | 2808 | 1620 | 3132 |
| 2 | 1404 | 810 | 1566 |
| 3 | 702 | 405 | 783 |
| 3 | 234 | 135 | 261 |
| 3 | 78 | 45 | 87 |
| 26 | 15 | 29 |
Step 7 : Number 26, 15 and 29, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot3\cdot3 = 108 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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