Step 1 :
Divide $ 27182 $ by $ 3141 $ and get the remainder

$$ 27182 : 3141 = 8 \text{ ( remainder is } \color{blue}{ 2054 } \text{ ) } $$

The remainder is positive ($ 2054 > 0 $), so we will continue with division.

Step 2 :
Divide $ 3141 $ by $ \color{blue}{ 2054 } $ and get the remainder

$$ 3141 : 2054 = 1 \text{ ( remainder is } \color{blue}{ 1087 } \text{ ) } $$

The remainder is still positive ($ 1087 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2054 $ by $ \color{blue}{ 1087 } $ and get the remainder

$$ 2054 : 1087 = 1 \text{ ( remainder is } \color{blue}{ 967 } \text{ ) } $$

The remainder is still positive ($ 967 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1087 $ by $ \color{blue}{ 967 } $ and get the remainder

$$ 1087 : 967 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 5 :
Divide $ 967 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 967 : 120 = 8 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 6 :
Divide $ 120 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 120 : 7 = 17 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 7 : \color{blue}{ \boxed { 1 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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