Step 1 :
Divide $ 831 $ by $ 178 $ and get the remainder

$$ 831 : 178 = 4 \text{ ( remainder is } \color{blue}{ 119 } \text{ ) } $$

The remainder is positive ($ 119 > 0 $), so we will continue with division.

Step 2 :
Divide $ 178 $ by $ \color{blue}{ 119 } $ and get the remainder

$$ 178 : 119 = 1 \text{ ( remainder is } \color{blue}{ 59 } \text{ ) } $$

The remainder is still positive ($ 59 > 0 $), so we will continue with division.

Step 3 :
Divide $ 119 $ by $ \color{blue}{ 59 } $ and get the remainder

$$ 119 : 59 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
Divide $ 59 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 59 : \color{blue}{ \boxed { 1 }} = 59 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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