Question
Find Greatest Common Divisor of 270 and 450, using repeated division.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 : Place the numbers inside division bar:.
| 270 | 450 |
Step 2 : Divide numbers by 2.
| 2 | 270 | 450 |
| 135 | 225 |
Step 3 : Divide numbers by 3.
| 2 | 270 | 450 |
| 3 | 135 | 225 |
| 45 | 75 |
Step 4 : Divide numbers by 3.
| 2 | 270 | 450 |
| 3 | 135 | 225 |
| 3 | 45 | 75 |
| 15 | 25 |
Step 5 : Number 15 and 25, 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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