Step 1 : Find prime factorization of each number.

$$\begin{aligned}6724520 =& 2\cdot2\cdot2\cdot5\cdot11\cdot17\cdot29\cdot31\\[8pt]26978328 =& 2\cdot2\cdot2\cdot3\cdot3\cdot13\cdot19\cdot37\cdot41\\[8pt]\end{aligned}$$

(view steps on how to factor 6724520 and 26978328. )

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

$$\begin{aligned}6724520 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot5\cdot11\cdot17\cdot29\cdot31\\[8pt]26978328 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot3\cdot3\cdot13\cdot19\cdot37\cdot41\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2 = 8 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator