Step 1 : Find prime factorization of each number.

$$\begin{aligned}142766 =& 2\cdot13\cdot17\cdot17\cdot19\\[8pt]1729 =& 7\cdot13\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 142766 and 1729. )

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

$$\begin{aligned}142766 =& 2\cdot\color{blue}{\boxed{13}}\cdot17\cdot17\cdot\color{red}{\boxed{19}}\\[8pt]1729 =& 7\cdot\color{blue}{\boxed{13}}\cdot\color{red}{\boxed{19}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 13\cdot19 = 247 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator