Step 1 :
Divide $ 11476 $ by $ 683 $ and get the remainder

$$ 11476 : 683 = 16 \text{ ( remainder is } \color{blue}{ 548 } \text{ ) } $$

The remainder is positive ($ 548 > 0 $), so we will continue with division.

Step 2 :
Divide $ 683 $ by $ \color{blue}{ 548 } $ and get the remainder

$$ 683 : 548 = 1 \text{ ( remainder is } \color{blue}{ 135 } \text{ ) } $$

The remainder is still positive ($ 135 > 0 $), so we will continue with division.

Step 3 :
Divide $ 548 $ by $ \color{blue}{ 135 } $ and get the remainder

$$ 548 : 135 = 4 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 135 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 135 : 8 = 16 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 8 : 7 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 7 : \color{blue}{ \boxed { 1 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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