Question
Find Greatest Common Divisor of 513, 1134 and 1215, using repeated division.
Answer
The GCD of given numbers is 27.
Explanation
Step 1 : Place the numbers inside division bar:.
| 513 | 1134 | 1215 |
Step 2 : Divide numbers by 3.
| 3 | 513 | 1134 | 1215 |
| 171 | 378 | 405 |
Step 3 : Divide numbers by 3.
| 3 | 513 | 1134 | 1215 |
| 3 | 171 | 378 | 405 |
| 57 | 126 | 135 |
Step 4 : Divide numbers by 3.
| 3 | 513 | 1134 | 1215 |
| 3 | 171 | 378 | 405 |
| 3 | 57 | 126 | 135 |
| 19 | 42 | 45 |
Step 5 : Number 19, 42 and 45, cannot be divided any more. The GCD is:
$$ GCD = 3\cdot3\cdot3 = 27 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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