The GCD of given numbers is 143.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1573 =& 11\cdot11\cdot13\\[8pt]2145 =& 3\cdot5\cdot11\cdot13\\[8pt]\end{aligned}$$(view steps on how to factor 1573 and 2145. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1573 =& \color{blue}{\boxed{11}}\cdot11\cdot\color{red}{\boxed{13}}\\[8pt]2145 =& 3\cdot5\cdot\color{blue}{\boxed{11}}\cdot\color{red}{\boxed{13}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 11\cdot13 = 143 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.