Step 1 :
Divide $ 15790 $ by $ 10790 $ and get the remainder

$$ 15790 : 10790 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 10790 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10790 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 790 } \text{ ) } $$

The remainder is still positive ($ 790 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 790 } $ and get the remainder

$$ 5000 : 790 = 6 \text{ ( remainder is } \color{blue}{ 260 } \text{ ) } $$

The remainder is still positive ($ 260 > 0 $), so we will continue with division.

Step 4 :
Divide $ 790 $ by $ \color{blue}{ 260 } $ and get the remainder

$$ 790 : 260 = 3 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 5 :
Divide $ 260 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 260 : \color{blue}{ \boxed { 10 }} = 26 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator