Step 1 :
Divide $ 3605 $ by $ 371 $ and get the remainder

$$ 3605 : 371 = 9 \text{ ( remainder is } \color{blue}{ 266 } \text{ ) } $$

The remainder is positive ($ 266 > 0 $), so we will continue with division.

Step 2 :
Divide $ 371 $ by $ \color{blue}{ 266 } $ and get the remainder

$$ 371 : 266 = 1 \text{ ( remainder is } \color{blue}{ 105 } \text{ ) } $$

The remainder is still positive ($ 105 > 0 $), so we will continue with division.

Step 3 :
Divide $ 266 $ by $ \color{blue}{ 105 } $ and get the remainder

$$ 266 : 105 = 2 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

The remainder is still positive ($ 56 > 0 $), so we will continue with division.

Step 4 :
Divide $ 105 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 105 : 56 = 1 \text{ ( remainder is } \color{blue}{ 49 } \text{ ) } $$

The remainder is still positive ($ 49 > 0 $), so we will continue with division.

Step 5 :
Divide $ 56 $ by $ \color{blue}{ 49 } $ and get the remainder

$$ 56 : 49 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 6 :
Divide $ 49 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 49 : \color{blue}{ \boxed { 7 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator