Step 1 :
Divide $ 2592 $ by $ 2501 $ and get the remainder

$$ 2592 : 2501 = 1 \text{ ( remainder is } \color{blue}{ 91 } \text{ ) } $$

The remainder is positive ($ 91 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2501 $ by $ \color{blue}{ 91 } $ and get the remainder

$$ 2501 : 91 = 27 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

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

Step 3 :
Divide $ 91 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 91 : 44 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 4 :
Divide $ 44 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 44 : 3 = 14 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator