Step 1 :
Divide $31415$ by $14142$ and get the remainder

The remainder is positive ($3131>0$), so we will continue with division.

Step 2 :
Divide $14142$ by $3131$ and get the remainder

The remainder is still positive ($1618>0$), so we will continue with division.

Step 3 :
Divide $3131$ by $1618$ and get the remainder

The remainder is still positive ($1513>0$), so we will continue with division.

Step 4 :
Divide $1618$ by $1513$ and get the remainder

The remainder is still positive ($105>0$), so we will continue with division.

Step 5 :
Divide $1513$ by $105$ and get the remainder

The remainder is still positive ($43>0$), so we will continue with division.

Step 6 :
Divide $105$ by $43$ and get the remainder

The remainder is still positive ($19>0$), so we will continue with division.

Step 7 :
Divide $43$ by $19$ and get the remainder

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

Step 8 :
Divide $19$ by $5$ and get the remainder

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

Step 9 :
Divide $5$ by $4$ and get the remainder

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

Step 10 :
Divide $4$ 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.