Step 1 :
Divide $ 3568 $ by $ 1604 $ and get the remainder

$$ 3568 : 1604 = 2 \text{ ( remainder is } \color{blue}{ 360 } \text{ ) } $$

The remainder is positive ($ 360 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1604 $ by $ \color{blue}{ 360 } $ and get the remainder

$$ 1604 : 360 = 4 \text{ ( remainder is } \color{blue}{ 164 } \text{ ) } $$

The remainder is still positive ($ 164 > 0 $), so we will continue with division.

Step 3 :
Divide $ 360 $ by $ \color{blue}{ 164 } $ and get the remainder

$$ 360 : 164 = 2 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 4 :
Divide $ 164 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 164 : 32 = 5 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 5 :
Divide $ 32 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 32 : \color{blue}{ \boxed { 4 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator