Step 1 :
Divide $ 232804 $ by $ 208754 $ and get the remainder

$$ 232804 : 208754 = 1 \text{ ( remainder is } \color{blue}{ 24050 } \text{ ) } $$

The remainder is positive ($ 24050 > 0 $), so we will continue with division.

Step 2 :
Divide $ 208754 $ by $ \color{blue}{ 24050 } $ and get the remainder

$$ 208754 : 24050 = 8 \text{ ( remainder is } \color{blue}{ 16354 } \text{ ) } $$

The remainder is still positive ($ 16354 > 0 $), so we will continue with division.

Step 3 :
Divide $ 24050 $ by $ \color{blue}{ 16354 } $ and get the remainder

$$ 24050 : 16354 = 1 \text{ ( remainder is } \color{blue}{ 7696 } \text{ ) } $$

The remainder is still positive ($ 7696 > 0 $), so we will continue with division.

Step 4 :
Divide $ 16354 $ by $ \color{blue}{ 7696 } $ and get the remainder

$$ 16354 : 7696 = 2 \text{ ( remainder is } \color{blue}{ 962 } \text{ ) } $$

The remainder is still positive ($ 962 > 0 $), so we will continue with division.

Step 5 :
Divide $ 7696 $ by $ \color{blue}{ 962 } $ and get the remainder

$$ 7696 : \color{blue}{ \boxed { 962 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 962 }} $.

This solution can be visualized using a Venn diagram.

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

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