Step 1 :
Divide $ 5000 $ by $ 3000 $ and get the remainder

$$ 5000 : 3000 = 1 \text{ ( remainder is } \color{blue}{ 2000 } \text{ ) } $$

The remainder is positive ($ 2000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 3000 $ by $ \color{blue}{ 2000 } $ and get the remainder

$$ 3000 : 2000 = 1 \text{ ( remainder is } \color{blue}{ 1000 } \text{ ) } $$

The remainder is still positive ($ 1000 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2000 $ by $ \color{blue}{ 1000 } $ and get the remainder

$$ 2000 : \color{blue}{ \boxed { 1000 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1000 }} $.

This solution can be visualized using a Venn diagram.

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

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