Step 1 :
Divide $ 390 $ by $ 58 $ and get the remainder

$$ 390 : 58 = 6 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is positive ($ 42 > 0 $), so we will continue with division.

Step 2 :
Divide $ 58 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 58 : 42 = 1 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 3 :
Divide $ 42 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 42 : 16 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 4 :
Divide $ 16 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 16 : 10 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 5 :
Divide $ 10 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 10 : 6 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

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

$$ 6 : 4 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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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