Step 1 : Find prime factorization of each number.

$$\begin{aligned}819514390 =& 2\cdot5\cdot421\cdot194659\\[8pt]869246761 =& 7393\cdot117577\\[8pt]\end{aligned}$$

(view steps on how to factor 819514390 and 869246761. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}819514390 =& 2\cdot5\cdot421\cdot194659\\[8pt]869246761 =& 7393\cdot117577\\[8pt]\end{aligned}$$

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator