The GCD of given numbers is 37.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}296 =& 2\cdot2\cdot2\cdot37\\[8pt]703 =& 19\cdot37\\[8pt]814 =& 2\cdot11\cdot37\\[8pt]\end{aligned}$$(view steps on how to factor 296, 703 and 814. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}296 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{37}}\\[8pt]703 =& 19\cdot\color{blue}{\boxed{37}}\\[8pt]814 =& 2\cdot11\cdot\color{blue}{\boxed{37}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 37 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.