Step 1 :
Divide $ 2013 $ by $ 113 $ and get the remainder

$$ 2013 : 113 = 17 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is positive ($ 92 > 0 $), so we will continue with division.

Step 2 :
Divide $ 113 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 113 : 92 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 3 :
Divide $ 92 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 92 : 21 = 4 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 21 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 21 : 8 = 2 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 8 : 5 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 6 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 5 : 3 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 8 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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