Step 1 :
Divide $ 26169 $ by $ 12760 $ and get the remainder

$$ 26169 : 12760 = 2 \text{ ( remainder is } \color{blue}{ 649 } \text{ ) } $$

The remainder is positive ($ 649 > 0 $), so we will continue with division.

Step 2 :
Divide $ 12760 $ by $ \color{blue}{ 649 } $ and get the remainder

$$ 12760 : 649 = 19 \text{ ( remainder is } \color{blue}{ 429 } \text{ ) } $$

The remainder is still positive ($ 429 > 0 $), so we will continue with division.

Step 3 :
Divide $ 649 $ by $ \color{blue}{ 429 } $ and get the remainder

$$ 649 : 429 = 1 \text{ ( remainder is } \color{blue}{ 220 } \text{ ) } $$

The remainder is still positive ($ 220 > 0 $), so we will continue with division.

Step 4 :
Divide $ 429 $ by $ \color{blue}{ 220 } $ and get the remainder

$$ 429 : 220 = 1 \text{ ( remainder is } \color{blue}{ 209 } \text{ ) } $$

The remainder is still positive ($ 209 > 0 $), so we will continue with division.

Step 5 :
Divide $ 220 $ by $ \color{blue}{ 209 } $ and get the remainder

$$ 220 : 209 = 1 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 6 :
Divide $ 209 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 209 : \color{blue}{ \boxed { 11 }} = 19 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator