The GCD of given numbers is 3.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}2517 =& 3\cdot839\\[8pt]2370 =& 2\cdot3\cdot5\cdot79\\[8pt]\end{aligned}$$(view steps on how to factor 2517 and 2370. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}2517 =& \color{blue}{\boxed{3}}\cdot839\\[8pt]2370 =& 2\cdot\color{blue}{\boxed{3}}\cdot5\cdot79\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.