Step 1 : Find prime factorization of each number.

$$\begin{aligned}5264 =& 2\cdot2\cdot2\cdot2\cdot7\cdot47\\[8pt]15472 =& 2\cdot2\cdot2\cdot2\cdot967\\[8pt]\end{aligned}$$

(view steps on how to factor 5264 and 15472. )

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

$$\begin{aligned}5264 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot7\cdot47\\[8pt]15472 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot967\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2 = 16 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator