Step 1 :
Divide $ 2020 $ by $ 458 $ and get the remainder

$$ 2020 : 458 = 4 \text{ ( remainder is } \color{blue}{ 188 } \text{ ) } $$

The remainder is positive ($ 188 > 0 $), so we will continue with division.

Step 2 :
Divide $ 458 $ by $ \color{blue}{ 188 } $ and get the remainder

$$ 458 : 188 = 2 \text{ ( remainder is } \color{blue}{ 82 } \text{ ) } $$

The remainder is still positive ($ 82 > 0 $), so we will continue with division.

Step 3 :
Divide $ 188 $ by $ \color{blue}{ 82 } $ and get the remainder

$$ 188 : 82 = 2 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

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

Step 4 :
Divide $ 82 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 82 : 24 = 3 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 5 :
Divide $ 24 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 24 : 10 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 6 :
Divide $ 10 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 10 : 4 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder

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

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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