Step 1 :
Divide $ 11058 $ by $ 9894 $ and get the remainder

$$ 11058 : 9894 = 1 \text{ ( remainder is } \color{blue}{ 1164 } \text{ ) } $$

The remainder is positive ($ 1164 > 0 $), so we will continue with division.

Step 2 :
Divide $ 9894 $ by $ \color{blue}{ 1164 } $ and get the remainder

$$ 9894 : 1164 = 8 \text{ ( remainder is } \color{blue}{ 582 } \text{ ) } $$

The remainder is still positive ($ 582 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1164 $ by $ \color{blue}{ 582 } $ and get the remainder

$$ 1164 : \color{blue}{ \boxed { 582 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 582 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator