Step 1 :
Divide $ 676 $ by $ 403 $ and get the remainder

$$ 676 : 403 = 1 \text{ ( remainder is } \color{blue}{ 273 } \text{ ) } $$

The remainder is positive ($ 273 > 0 $), so we will continue with division.

Step 2 :
Divide $ 403 $ by $ \color{blue}{ 273 } $ and get the remainder

$$ 403 : 273 = 1 \text{ ( remainder is } \color{blue}{ 130 } \text{ ) } $$

The remainder is still positive ($ 130 > 0 $), so we will continue with division.

Step 3 :
Divide $ 273 $ by $ \color{blue}{ 130 } $ and get the remainder

$$ 273 : 130 = 2 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 4 :
Divide $ 130 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 130 : \color{blue}{ \boxed { 13 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.

This solution can be visualized using a Venn diagram.

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

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