Step 1 : Find prime factorization of each number.

$$\begin{aligned}12954 =& 2\cdot3\cdot17\cdot127\\[8pt]12954 =& 2\cdot3\cdot17\cdot127\\[8pt]\end{aligned}$$

(view steps on how to factor 12954 and 12954. )

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

$$\begin{aligned}12954 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{17}}\cdot\color{Orange}{\boxed{127}}\\[8pt]12954 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{17}}\cdot\color{Orange}{\boxed{127}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot17\cdot127 = 12954 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator