Step 1 : Find prime factorization of each number.

$$\begin{aligned}2023 =& 7\cdot17\cdot17\\[8pt]4046 =& 2\cdot7\cdot17\cdot17\\[8pt]\end{aligned}$$

(view steps on how to factor 2023 and 4046. )

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

$$\begin{aligned}2023 =& \color{blue}{\boxed{7}}\cdot\color{red}{\boxed{17}}\cdot\color{Fuchsia}{\boxed{17}}\\[8pt]4046 =& 2\cdot\color{blue}{\boxed{7}}\cdot\color{red}{\boxed{17}}\cdot\color{Fuchsia}{\boxed{17}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 7\cdot17\cdot17 = 2023 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator