Step 1 :
Divide $ 588 $ by $ 92 $ and get the remainder

$$ 588 : 92 = 6 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is positive ($ 36 > 0 $), so we will continue with division.

Step 2 :
Divide $ 92 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 92 : 36 = 2 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 3 :
Divide $ 36 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 36 : 20 = 1 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 4 :
Divide $ 20 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 20 : 16 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 5 :
Divide $ 16 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 16 : \color{blue}{ \boxed { 4 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

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