Step 1 :
Divide $8496$ by $5234$ and get the remainder

The remainder is positive ($3262>0$), so we will continue with division.

Step 2 :
Divide $5234$ by $3262$ and get the remainder

The remainder is still positive ($1972>0$), so we will continue with division.

Step 3 :
Divide $3262$ by $1972$ and get the remainder

The remainder is still positive ($1290>0$), so we will continue with division.

Step 4 :
Divide $1972$ by $1290$ and get the remainder

The remainder is still positive ($682>0$), so we will continue with division.

Step 5 :
Divide $1290$ by $682$ and get the remainder

The remainder is still positive ($608>0$), so we will continue with division.

Step 6 :
Divide $682$ by $608$ and get the remainder

The remainder is still positive ($74>0$), so we will continue with division.

Step 7 :
Divide $608$ by $74$ and get the remainder

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

Step 8 :
Divide $74$ by $16$ and get the remainder

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

Step 9 :
Divide $16$ by $10$ and get the remainder

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

Step 10 :
Divide $10$ by $6$ and get the remainder

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

Step 11 :
Divide $6$ by $4$ and get the remainder

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

Step 12 :
Divide $4$ by $2$ and get the remainder

The remainder is zero => GCD is the last divisor $\boxed{2}$.

This solution can be visualized using a Venn diagram.

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