Find Greatest Common Divisor of 180 and 252, using Euclidean algorithm.

Answer

The GCD of given numbers is 36.

Step 1 :
Divide $ 252 $ by $ 180 $ and get the remainder

$$ 252 : 180 = 1 \text{ ( remainder is } \color{blue}{ 72 } \text{ ) } $$

The remainder is positive ($ 72 > 0 $), so we will continue with division.

Step 2 :
Divide $ 180 $ by $ \color{blue}{ 72 } $ and get the remainder

$$ 180 : 72 = 2 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is still positive ($ 36 > 0 $), so we will continue with division.

Step 3 :
Divide $ 72 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 72 : \color{blue}{ \boxed { 36 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 36 }} $.

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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