Question
Find Greatest Common Divisor of 2394 and 342, using repeated division.
Answer
The GCD of given numbers is 342.
Explanation
Step 1 : Place the numbers inside division bar:.
| 2394 | 342 |
Step 2 : Divide numbers by 2.
| 2 | 2394 | 342 |
| 1197 | 171 |
Step 3 : Divide numbers by 3.
| 2 | 2394 | 342 |
| 3 | 1197 | 171 |
| 399 | 57 |
Step 4 : Divide numbers by 3.
| 2 | 2394 | 342 |
| 3 | 1197 | 171 |
| 3 | 399 | 57 |
| 133 | 19 |
Step 5 : Divide numbers by 19.
| 2 | 2394 | 342 |
| 3 | 1197 | 171 |
| 3 | 399 | 57 |
| 19 | 133 | 19 |
| 7 | 1 |
Step 6 : Number 7 and 1, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3\cdot19 = 342 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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