Question
Find Greatest Common Divisor of 180 and 225, using repeated division.
Answer
The GCD of given numbers is 45.
Explanation
Step 1 : Place the numbers inside division bar:.
| 180 | 225 |
Step 2 : Divide numbers by 3.
| 3 | 180 | 225 |
| 60 | 75 |
Step 3 : Divide numbers by 3.
| 3 | 180 | 225 |
| 3 | 60 | 75 |
| 20 | 25 |
Step 4 : Divide numbers by 5.
| 3 | 180 | 225 |
| 3 | 60 | 75 |
| 5 | 20 | 25 |
| 4 | 5 |
Step 5 : Number 4 and 5, cannot be divided any more. The GCD is:
$$ GCD = 3\cdot3\cdot5 = 45 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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