Step 1 : Find prime factorization of each number.

$$\begin{aligned}232804 =& 2\cdot2\cdot11\cdot11\cdot13\cdot37\\[8pt]208754 =& 2\cdot7\cdot13\cdot31\cdot37\\[8pt]575498 =& 2\cdot7\cdot11\cdot37\cdot101\\[8pt]\end{aligned}$$

(view steps on how to factor 232804, 208754 and 575498. )

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

$$\begin{aligned}232804 =& \color{blue}{\boxed{2}}\cdot2\cdot11\cdot11\cdot13\cdot\color{red}{\boxed{37}}\\[8pt]208754 =& \color{blue}{\boxed{2}}\cdot7\cdot13\cdot31\cdot\color{red}{\boxed{37}}\\[8pt]575498 =& \color{blue}{\boxed{2}}\cdot7\cdot11\cdot\color{red}{\boxed{37}}\cdot101\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot37 = 74 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator