Step 1 : Find prime factorization of each number.

$$\begin{aligned}81719 =& 11\cdot17\cdot19\cdot23\\[8pt]52003 =& 7\cdot17\cdot19\cdot23\\[8pt]33649 =& 7\cdot11\cdot19\cdot23\\[8pt]30107 =& 7\cdot11\cdot17\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 81719, 52003, 33649 and 30107. )

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

$$\begin{aligned}81719 =& 11\cdot17\cdot19\cdot\color{blue}{\boxed{23}}\\[8pt]52003 =& 7\cdot17\cdot19\cdot\color{blue}{\boxed{23}}\\[8pt]33649 =& 7\cdot11\cdot19\cdot\color{blue}{\boxed{23}}\\[8pt]30107 =& 7\cdot11\cdot17\cdot\color{blue}{\boxed{23}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 23 $$

GCD Calculator