Step 1 : Find prime factorization of each number.

$$\begin{aligned}124523 =& 7\cdot17789\\[8pt]526387932 =& 2\cdot2\cdot3\cdot3\cdot7\cdot17\cdot19\cdot29\cdot223\\[8pt]\end{aligned}$$

(view steps on how to factor 124523 and 526387932. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}124523 =& \color{blue}{\boxed{7}}\cdot17789\\[8pt]526387932 =& 2\cdot2\cdot3\cdot3\cdot\color{blue}{\boxed{7}}\cdot17\cdot19\cdot29\cdot223\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 7 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator