Step 1 :
Divide $ 7756 $ by $ 6515 $ and get the remainder

$$ 7756 : 6515 = 1 \text{ ( remainder is } \color{blue}{ 1241 } \text{ ) } $$

The remainder is positive ($ 1241 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6515 $ by $ \color{blue}{ 1241 } $ and get the remainder

$$ 6515 : 1241 = 5 \text{ ( remainder is } \color{blue}{ 310 } \text{ ) } $$

The remainder is still positive ($ 310 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1241 $ by $ \color{blue}{ 310 } $ and get the remainder

$$ 1241 : 310 = 4 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
Divide $ 310 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 310 : \color{blue}{ \boxed { 1 }} = 310 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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