Question
Find Greatest Common Divisor of 81 and 108, using repeated division.
Answer
The GCD of given numbers is 27.
Explanation
Step 1 : Place the numbers inside division bar:.
| 81 | 108 |
Step 2 : Divide numbers by 3.
| 3 | 81 | 108 |
| 27 | 36 |
Step 3 : Divide numbers by 3.
| 3 | 81 | 108 |
| 3 | 27 | 36 |
| 9 | 12 |
Step 4 : Divide numbers by 3.
| 3 | 81 | 108 |
| 3 | 27 | 36 |
| 3 | 9 | 12 |
| 3 | 4 |
Step 5 : Number 3 and 4, 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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