Step 1 :
Divide $ 15635 $ by $ 2945 $ and get the remainder

$$ 15635 : 2945 = 5 \text{ ( remainder is } \color{blue}{ 910 } \text{ ) } $$

The remainder is positive ($ 910 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2945 $ by $ \color{blue}{ 910 } $ and get the remainder

$$ 2945 : 910 = 3 \text{ ( remainder is } \color{blue}{ 215 } \text{ ) } $$

The remainder is still positive ($ 215 > 0 $), so we will continue with division.

Step 3 :
Divide $ 910 $ by $ \color{blue}{ 215 } $ and get the remainder

$$ 910 : 215 = 4 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 4 :
Divide $ 215 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 215 : 50 = 4 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 5 :
Divide $ 50 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 50 : 15 = 3 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 6 :
Divide $ 15 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 15 : \color{blue}{ \boxed { 5 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator