Step 1 :
Divide $ 3026 $ by $ 258 $ and get the remainder

$$ 3026 : 258 = 11 \text{ ( remainder is } \color{blue}{ 188 } \text{ ) } $$

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

Step 2 :
Divide $ 258 $ by $ \color{blue}{ 188 } $ and get the remainder

$$ 258 : 188 = 1 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 3 :
Divide $ 188 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 188 : 70 = 2 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 4 :
Divide $ 70 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 70 : 48 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 5 :
Divide $ 48 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 48 : 22 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 6 :
Divide $ 22 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 22 : 4 = 5 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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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