Step 1 : Find prime factorization of each number.

$$\begin{aligned}1377 =& 3\cdot3\cdot3\cdot3\cdot17\\[8pt]1701 =& 3\cdot3\cdot3\cdot3\cdot3\cdot7\\[8pt]9477 =& 3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 1377, 1701 and 9477. )

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

$$\begin{aligned}1377 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{3}}\cdot17\\[8pt]1701 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{3}}\cdot3\cdot7\\[8pt]9477 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{3}}\cdot3\cdot3\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot3\cdot3\cdot3 = 81 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator