Question
Find Greatest Common Divisor of 1134 and 1386, using repeated division.
Answer
The GCD of given numbers is 126.
Explanation
Step 1 : Place the numbers inside division bar:.
| 1134 | 1386 |
Step 2 : Divide numbers by 2.
| 2 | 1134 | 1386 |
| 567 | 693 |
Step 3 : Divide numbers by 3.
| 2 | 1134 | 1386 |
| 3 | 567 | 693 |
| 189 | 231 |
Step 4 : Divide numbers by 3.
| 2 | 1134 | 1386 |
| 3 | 567 | 693 |
| 3 | 189 | 231 |
| 63 | 77 |
Step 5 : Divide numbers by 7.
| 2 | 1134 | 1386 |
| 3 | 567 | 693 |
| 3 | 189 | 231 |
| 7 | 63 | 77 |
| 9 | 11 |
Step 6 : Number 9 and 11, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3\cdot7 = 126 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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