Step 1 :
Divide $ 2059 $ by $ 581 $ and get the remainder

$$ 2059 : 581 = 3 \text{ ( remainder is } \color{blue}{ 316 } \text{ ) } $$

The remainder is positive ($ 316 > 0 $), so we will continue with division.

Step 2 :
Divide $ 581 $ by $ \color{blue}{ 316 } $ and get the remainder

$$ 581 : 316 = 1 \text{ ( remainder is } \color{blue}{ 265 } \text{ ) } $$

The remainder is still positive ($ 265 > 0 $), so we will continue with division.

Step 3 :
Divide $ 316 $ by $ \color{blue}{ 265 } $ and get the remainder

$$ 316 : 265 = 1 \text{ ( remainder is } \color{blue}{ 51 } \text{ ) } $$

The remainder is still positive ($ 51 > 0 $), so we will continue with division.

Step 4 :
Divide $ 265 $ by $ \color{blue}{ 51 } $ and get the remainder

$$ 265 : 51 = 5 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 5 :
Divide $ 51 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 51 : 10 = 5 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 10 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 1 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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