Step 1 :
Divide $ 2592 $ by $ 69 $ and get the remainder

$$ 2592 : 69 = 37 \text{ ( remainder is } \color{blue}{ 39 } \text{ ) } $$

The remainder is positive ($ 39 > 0 $), so we will continue with division.

Step 2 :
Divide $ 69 $ by $ \color{blue}{ 39 } $ and get the remainder

$$ 69 : 39 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 3 :
Divide $ 39 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 39 : 30 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 4 :
Divide $ 30 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 30 : 9 = 3 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 5 :
Divide $ 9 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 3 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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