Step 1 :
Divide $242040$ by $85672$ and get the remainder

The remainder is positive ($70696>0$), so we will continue with division.

Step 2 :
Divide $85672$ by $70696$ and get the remainder

The remainder is still positive ($14976>0$), so we will continue with division.

Step 3 :
Divide $70696$ by $14976$ and get the remainder

The remainder is still positive ($10792>0$), so we will continue with division.

Step 4 :
Divide $14976$ by $10792$ and get the remainder

The remainder is still positive ($4184>0$), so we will continue with division.

Step 5 :
Divide $10792$ by $4184$ and get the remainder

The remainder is still positive ($2424>0$), so we will continue with division.

Step 6 :
Divide $4184$ by $2424$ and get the remainder

The remainder is still positive ($1760>0$), so we will continue with division.

Step 7 :
Divide $2424$ by $1760$ and get the remainder

The remainder is still positive ($664>0$), so we will continue with division.

Step 8 :
Divide $1760$ by $664$ and get the remainder

The remainder is still positive ($432>0$), so we will continue with division.

Step 9 :
Divide $664$ by $432$ and get the remainder

The remainder is still positive ($232>0$), so we will continue with division.

Step 10 :
Divide $432$ by $232$ and get the remainder

The remainder is still positive ($200>0$), so we will continue with division.

Step 11 :
Divide $232$ by $200$ and get the remainder

The remainder is still positive ($32>0$), so we will continue with division.

Step 12 :
Divide $200$ by $32$ and get the remainder

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

Step 13 :
Divide $32$ by $8$ and get the remainder

The remainder is zero => GCD is the last divisor $\boxed{8}$.

This solution can be visualized using a Venn diagram.

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