Step 1 :
Divide $ 299 $ by $ 256 $ and get the remainder

$$ 299 : 256 = 1 \text{ ( remainder is } \color{blue}{ 43 } \text{ ) } $$

The remainder is positive ($ 43 > 0 $), so we will continue with division.

Step 2 :
Divide $ 256 $ by $ \color{blue}{ 43 } $ and get the remainder

$$ 256 : 43 = 5 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

The remainder is still positive ($ 41 > 0 $), so we will continue with division.

Step 3 :
Divide $ 43 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 43 : 41 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 4 :
Divide $ 41 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 41 : 2 = 20 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 5 :
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.

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