The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}453 =& 3\cdot151\\[8pt]827 =& 827\\[8pt]501 =& 3\cdot167\\[8pt]952 =& 2\cdot2\cdot2\cdot7\cdot17\\[8pt]\end{aligned}$$(view steps on how to factor 453, 827, 501 and 952. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}453 =& 3\cdot151\\[8pt]827 =& 827\\[8pt]501 =& 3\cdot167\\[8pt]952 =& 2\cdot2\cdot2\cdot7\cdot17\\[8pt]\end{aligned}$$Note that in this example numbers do not have any common factors.
Step 3 : Multiply the boxed numbers together:
Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.