Find Greatest Common Divisor of 240 and 180, using Euclidean algorithm.
Answer
The GCD of given numbers is 60.
Explanation
Step 1 :
Divide $ 240 $ by $ 180 $ and get the remainder
The remainder is positive ($ 60 > 0 $), so we will continue with division.
Step 2 :
Divide $ 180 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 60 }} $.
We can summarize an algorithm into a following table.
| 240 | : | 180 | = | 1 | remainder ( 60 ) | ||
| 180 | : | 60 | = | 3 | remainder ( 0 ) | ||
| GCD = 60 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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