The GCD of given numbers is 2.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}955445098 =& 2\cdot53\cdot103\cdot87511\\[8pt]427525248 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot17\cdot79\cdot829\\[8pt]\end{aligned}$$(view steps on how to factor 955445098 and 427525248. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}955445098 =& \color{blue}{\boxed{2}}\cdot53\cdot103\cdot87511\\[8pt]427525248 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot17\cdot79\cdot829\\[8pt]\end{aligned}$$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.