Step 1 :
Divide $23883$ by $12409$ and get the remainder

The remainder is positive ($11474>0$), so we will continue with division.

Step 2 :
Divide $12409$ by $11474$ and get the remainder

The remainder is still positive ($935>0$), so we will continue with division.

Step 3 :
Divide $11474$ by $935$ and get the remainder

The remainder is still positive ($254>0$), so we will continue with division.

Step 4 :
Divide $935$ by $254$ and get the remainder

The remainder is still positive ($173>0$), so we will continue with division.

Step 5 :
Divide $254$ by $173$ and get the remainder

The remainder is still positive ($81>0$), so we will continue with division.

Step 6 :
Divide $173$ by $81$ and get the remainder

The remainder is still positive ($11>0$), so we will continue with division.

Step 7 :
Divide $81$ by $11$ and get the remainder

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

Step 8 :
Divide $11$ by $4$ and get the remainder

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

Step 9 :
Divide $4$ by $3$ and get the remainder

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

Step 10 :
Divide $3$ by $1$ and get the remainder

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

This solution can be visualized using a Venn diagram.

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