Step 1 :
Divide $ 2002 $ by $ 462 $ and get the remainder

$$ 2002 : 462 = 4 \text{ ( remainder is } \color{blue}{ 154 } \text{ ) } $$

The remainder is positive ($ 154 > 0 $), so we will continue with division.

Step 2 :
Divide $ 462 $ by $ \color{blue}{ 154 } $ and get the remainder

$$ 462 : \color{blue}{ \boxed { 154 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 154 }} $.

This solution can be visualized using a Venn diagram.

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

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