Step 1 :
Divide $ 729 $ by $ 256 $ and get the remainder

$$ 729 : 256 = 2 \text{ ( remainder is } \color{blue}{ 217 } \text{ ) } $$

The remainder is positive ($ 217 > 0 $), so we will continue with division.

Step 2 :
Divide $ 256 $ by $ \color{blue}{ 217 } $ and get the remainder

$$ 256 : 217 = 1 \text{ ( remainder is } \color{blue}{ 39 } \text{ ) } $$

The remainder is still positive ($ 39 > 0 $), so we will continue with division.

Step 3 :
Divide $ 217 $ by $ \color{blue}{ 39 } $ and get the remainder

$$ 217 : 39 = 5 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 4 :
Divide $ 39 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 39 : 22 = 1 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 5 :
Divide $ 22 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 22 : 17 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 6 :
Divide $ 17 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 17 : 5 = 3 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 5 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 5 : 2 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
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