The GCD of given numbers is 1078.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1160718174 =& 2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot7\cdot7\cdot7\cdot11\cdot211\\[8pt]316258250 =& 2\cdot5\cdot5\cdot5\cdot7\cdot7\cdot11\cdot2347\\[8pt]\end{aligned}$$(view steps on how to factor 1160718174 and 316258250. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1160718174 =& \color{blue}{\boxed{2}}\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{7}}\cdot7\cdot\color{Orange}{\boxed{11}}\cdot211\\[8pt]316258250 =& \color{blue}{\boxed{2}}\cdot5\cdot5\cdot5\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{7}}\cdot\color{Orange}{\boxed{11}}\cdot2347\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot7\cdot7\cdot11 = 1078 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.