Step 1 :
Divide $ 112 $ by $ 30 $ and get the remainder

$$ 112 : 30 = 3 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is positive ($ 22 > 0 $), so we will continue with division.

Step 2 :
Divide $ 30 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 30 : 22 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 3 :
Divide $ 22 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 22 : 8 = 2 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 4 :
Divide $ 8 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 8 : 6 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 5 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 2 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator