Question
Find Greatest Common Divisor of 54, 84 and 108, using repeated division.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 : Place the numbers inside division bar:.
| 54 | 84 | 108 |
Step 2 : Divide numbers by 2.
| 2 | 54 | 84 | 108 |
| 27 | 42 | 54 |
Step 3 : Divide numbers by 3.
| 2 | 54 | 84 | 108 |
| 3 | 27 | 42 | 54 |
| 9 | 14 | 18 |
Step 4 : Number 9, 14 and 18, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3 = 6 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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