Step 1 : Find prime factorization of each number.

$$\begin{aligned}1448 =& 2\cdot2\cdot2\cdot181\\[8pt]808 =& 2\cdot2\cdot2\cdot101\\[8pt]\end{aligned}$$

(view steps on how to factor 1448 and 808. )

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

$$\begin{aligned}1448 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot181\\[8pt]808 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot101\\[8pt]\end{aligned}$$

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