Step 1 :
Divide $ 3171 $ by $ 841 $ and get the remainder

$$ 3171 : 841 = 3 \text{ ( remainder is } \color{blue}{ 648 } \text{ ) } $$

The remainder is positive ($ 648 > 0 $), so we will continue with division.

Step 2 :
Divide $ 841 $ by $ \color{blue}{ 648 } $ and get the remainder

$$ 841 : 648 = 1 \text{ ( remainder is } \color{blue}{ 193 } \text{ ) } $$

The remainder is still positive ($ 193 > 0 $), so we will continue with division.

Step 3 :
Divide $ 648 $ by $ \color{blue}{ 193 } $ and get the remainder

$$ 648 : 193 = 3 \text{ ( remainder is } \color{blue}{ 69 } \text{ ) } $$

The remainder is still positive ($ 69 > 0 $), so we will continue with division.

Step 4 :
Divide $ 193 $ by $ \color{blue}{ 69 } $ and get the remainder

$$ 193 : 69 = 2 \text{ ( remainder is } \color{blue}{ 55 } \text{ ) } $$

The remainder is still positive ($ 55 > 0 $), so we will continue with division.

Step 5 :
Divide $ 69 $ by $ \color{blue}{ 55 } $ and get the remainder

$$ 69 : 55 = 1 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 6 :
Divide $ 55 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 55 : 14 = 3 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 7 :
Divide $ 14 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 14 : 13 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 8 :
Divide $ 13 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 13 : \color{blue}{ \boxed { 1 }} = 13 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator