Step 1 :
Divide $ 254 $ by $ 100 $ and get the remainder

$$ 254 : 100 = 2 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is positive ($ 54 > 0 $), so we will continue with division.

Step 2 :
Divide $ 100 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 100 : 54 = 1 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 3 :
Divide $ 54 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 54 : 46 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 46 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 46 : 8 = 5 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 8 : 6 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

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

$$ 6 : \color{blue}{ \boxed { 2 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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