Question
Find Greatest Common Divisor of 126 and 18, using repeated division.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 : Place the numbers inside division bar:.
| 126 | 18 |
Step 2 : Divide numbers by 2.
| 2 | 126 | 18 |
| 63 | 9 |
Step 3 : Divide numbers by 3.
| 2 | 126 | 18 |
| 3 | 63 | 9 |
| 21 | 3 |
Step 4 : Divide numbers by 3.
| 2 | 126 | 18 |
| 3 | 63 | 9 |
| 3 | 21 | 3 |
| 7 | 1 |
Step 5 : Number 7 and 1, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3 = 18 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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