Step 1 :
Divide $ 2406 $ by $ 654 $ and get the remainder

$$ 2406 : 654 = 3 \text{ ( remainder is } \color{blue}{ 444 } \text{ ) } $$

The remainder is positive ($ 444 > 0 $), so we will continue with division.

Step 2 :
Divide $ 654 $ by $ \color{blue}{ 444 } $ and get the remainder

$$ 654 : 444 = 1 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 3 :
Divide $ 444 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 444 : 210 = 2 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

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

Step 4 :
Divide $ 210 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 210 : 24 = 8 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 5 :
Divide $ 24 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 24 : 18 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 6 :
Divide $ 18 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 18 : \color{blue}{ \boxed { 6 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.

This solution can be visualized using a Venn diagram.

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

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