Step 1 :
Divide $ 831 $ by $ 172 $ and get the remainder

$$ 831 : 172 = 4 \text{ ( remainder is } \color{blue}{ 143 } \text{ ) } $$

The remainder is positive ($ 143 > 0 $), so we will continue with division.

Step 2 :
Divide $ 172 $ by $ \color{blue}{ 143 } $ and get the remainder

$$ 172 : 143 = 1 \text{ ( remainder is } \color{blue}{ 29 } \text{ ) } $$

The remainder is still positive ($ 29 > 0 $), so we will continue with division.

Step 3 :
Divide $ 143 $ by $ \color{blue}{ 29 } $ and get the remainder

$$ 143 : 29 = 4 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 4 :
Divide $ 29 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 29 : 27 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 27 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 27 : 2 = 13 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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