Step 1 :
Divide $ 108 $ by $ 10 $ and get the remainder

$$ 108 : 10 = 10 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 2 :
Divide $ 10 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 10 : 8 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 3 :
Divide $ 8 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 2 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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