Find Greatest Common Divisor of 324, 378 and 1890, using repeated division.
Answer
The GCD of given numbers is 54.
Explanation
Step 1 : Place the numbers inside division bar:.
| 324 | 378 | 1890 |
Step 2 : Divide numbers by 2.
| 2 | 324 | 378 | 1890 |
| 162 | 189 | 945 |
Step 3 : Divide numbers by 3.
| 2 | 324 | 378 | 1890 |
| 3 | 162 | 189 | 945 |
| 54 | 63 | 315 |
Step 4 : Divide numbers by 3.
| 2 | 324 | 378 | 1890 |
| 3 | 162 | 189 | 945 |
| 3 | 54 | 63 | 315 |
| 18 | 21 | 105 |
Step 5 : Divide numbers by 3.
| 2 | 324 | 378 | 1890 |
| 3 | 162 | 189 | 945 |
| 3 | 54 | 63 | 315 |
| 3 | 18 | 21 | 105 |
| 6 | 7 | 35 |
Step 6 : Number 6, 7 and 35, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3\cdot3 = 54 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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