The GCD of given numbers is 37.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}4884 =& 2\cdot2\cdot3\cdot11\cdot37\\[8pt]5365 =& 5\cdot29\cdot37\\[8pt]\end{aligned}$$(view steps on how to factor 4884 and 5365. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}4884 =& 2\cdot2\cdot3\cdot11\cdot\color{blue}{\boxed{37}}\\[8pt]5365 =& 5\cdot29\cdot\color{blue}{\boxed{37}}\\[8pt]\end{aligned}$$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.