Step 1 :
Divide $ 1071 $ by $ 577 $ and get the remainder

$$ 1071 : 577 = 1 \text{ ( remainder is } \color{blue}{ 494 } \text{ ) } $$

The remainder is positive ($ 494 > 0 $), so we will continue with division.

Step 2 :
Divide $ 577 $ by $ \color{blue}{ 494 } $ and get the remainder

$$ 577 : 494 = 1 \text{ ( remainder is } \color{blue}{ 83 } \text{ ) } $$

The remainder is still positive ($ 83 > 0 $), so we will continue with division.

Step 3 :
Divide $ 494 $ by $ \color{blue}{ 83 } $ and get the remainder

$$ 494 : 83 = 5 \text{ ( remainder is } \color{blue}{ 79 } \text{ ) } $$

The remainder is still positive ($ 79 > 0 $), so we will continue with division.

Step 4 :
Divide $ 83 $ by $ \color{blue}{ 79 } $ and get the remainder

$$ 83 : 79 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 5 :
Divide $ 79 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 79 : 4 = 19 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 6 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 4 : 3 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator