Step 1 :
Divide $ 1276 $ by $ 873 $ and get the remainder

$$ 1276 : 873 = 1 \text{ ( remainder is } \color{blue}{ 403 } \text{ ) } $$

The remainder is positive ($ 403 > 0 $), so we will continue with division.

Step 2 :
Divide $ 873 $ by $ \color{blue}{ 403 } $ and get the remainder

$$ 873 : 403 = 2 \text{ ( remainder is } \color{blue}{ 67 } \text{ ) } $$

The remainder is still positive ($ 67 > 0 $), so we will continue with division.

Step 3 :
Divide $ 403 $ by $ \color{blue}{ 67 } $ and get the remainder

$$ 403 : 67 = 6 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
Divide $ 67 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 67 : \color{blue}{ \boxed { 1 }} = 67 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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