The GCD of given numbers is 2.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}456 =& 2\cdot2\cdot2\cdot3\cdot19\\[8pt]788 =& 2\cdot2\cdot197\\[8pt]782 =& 2\cdot17\cdot23\\[8pt]\end{aligned}$$(view steps on how to factor 456, 788 and 782. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}456 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot3\cdot19\\[8pt]788 =& \color{blue}{\boxed{2}}\cdot2\cdot197\\[8pt]782 =& \color{blue}{\boxed{2}}\cdot17\cdot23\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.