Find Greatest Common Divisor of 135 and 180, using Euclidean algorithm.
Answer
The GCD of given numbers is 45.
Explanation
Step 1 :
Divide $ 180 $ by $ 135 $ and get the remainder
The remainder is positive ($ 45 > 0 $), so we will continue with division.
Step 2 :
Divide $ 135 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 45 }} $.
We can summarize an algorithm into a following table.
| 180 | : | 135 | = | 1 | remainder ( 45 ) | ||
| 135 | : | 45 | = | 3 | remainder ( 0 ) | ||
| GCD = 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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