Step 1 : Find prime factorization of each number.

$$\begin{aligned}542832 =& 2\cdot2\cdot2\cdot2\cdot3\cdot43\cdot263\\[8pt]184756 =& 2\cdot2\cdot11\cdot13\cdot17\cdot19\\[8pt]360864 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\cdot179\\[8pt]\end{aligned}$$

(view steps on how to factor 542832, 184756 and 360864. )

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

$$\begin{aligned}542832 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot3\cdot43\cdot263\\[8pt]184756 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot11\cdot13\cdot17\cdot19\\[8pt]360864 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\cdot179\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2 = 4 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator