Step 1 :
Divide $ 2592 $ by $ 2543 $ and get the remainder

$$ 2592 : 2543 = 1 \text{ ( remainder is } \color{blue}{ 49 } \text{ ) } $$

The remainder is positive ($ 49 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2543 $ by $ \color{blue}{ 49 } $ and get the remainder

$$ 2543 : 49 = 51 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

The remainder is still positive ($ 44 > 0 $), so we will continue with division.

Step 3 :
Divide $ 49 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 49 : 44 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 4 :
Divide $ 44 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 44 : 5 = 8 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

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

$$ 5 : 4 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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