Step 1 :
Divide $1970$ by $1066$ and get the remainder

The remainder is positive ($904>0$), so we will continue with division.

Step 2 :
Divide $1066$ by $904$ and get the remainder

The remainder is still positive ($162>0$), so we will continue with division.

Step 3 :
Divide $904$ by $162$ and get the remainder

The remainder is still positive ($94>0$), so we will continue with division.

Step 4 :
Divide $162$ by $94$ and get the remainder

The remainder is still positive ($68>0$), so we will continue with division.

Step 5 :
Divide $94$ by $68$ and get the remainder

The remainder is still positive ($26>0$), so we will continue with division.

Step 6 :
Divide $68$ by $26$ and get the remainder

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

Step 7 :
Divide $26$ by $16$ and get the remainder

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

Step 8 :
Divide $16$ by $10$ and get the remainder

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

Step 9 :
Divide $10$ by $6$ and get the remainder

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

Step 10 :
Divide $6$ by $4$ and get the remainder

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

Step 11 :
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.