Step 1 :
Divide $ 581 $ by $ 397 $ and get the remainder

$$ 581 : 397 = 1 \text{ ( remainder is } \color{blue}{ 184 } \text{ ) } $$

The remainder is positive ($ 184 > 0 $), so we will continue with division.

Step 2 :
Divide $ 397 $ by $ \color{blue}{ 184 } $ and get the remainder

$$ 397 : 184 = 2 \text{ ( remainder is } \color{blue}{ 29 } \text{ ) } $$

The remainder is still positive ($ 29 > 0 $), so we will continue with division.

Step 3 :
Divide $ 184 $ by $ \color{blue}{ 29 } $ and get the remainder

$$ 184 : 29 = 6 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 4 :
Divide $ 29 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 29 : 10 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 10 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 10 : 9 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 6 :
Divide $ 9 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 1 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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