Step 1 :
Divide $ 672 $ by $ 408 $ and get the remainder

$$ 672 : 408 = 1 \text{ ( remainder is } \color{blue}{ 264 } \text{ ) } $$

The remainder is positive ($ 264 > 0 $), so we will continue with division.

Step 2 :
Divide $ 408 $ by $ \color{blue}{ 264 } $ and get the remainder

$$ 408 : 264 = 1 \text{ ( remainder is } \color{blue}{ 144 } \text{ ) } $$

The remainder is still positive ($ 144 > 0 $), so we will continue with division.

Step 3 :
Divide $ 264 $ by $ \color{blue}{ 144 } $ and get the remainder

$$ 264 : 144 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 4 :
Divide $ 144 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 144 : 120 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 5 :
Divide $ 120 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 120 : \color{blue}{ \boxed { 24 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.

This solution can be visualized using a Venn diagram.

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

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