Step 1 : Find prime factorization of each number.

$$\begin{aligned}1386 =& 2\cdot3\cdot3\cdot7\cdot11\\[8pt]924 =& 2\cdot2\cdot3\cdot7\cdot11\\[8pt]660 =& 2\cdot2\cdot3\cdot5\cdot11\\[8pt]495 =& 3\cdot3\cdot5\cdot11\\[8pt]385 =& 5\cdot7\cdot11\\[8pt]308 =& 2\cdot2\cdot7\cdot11\\[8pt]252 =& 2\cdot2\cdot3\cdot3\cdot7\\[8pt]2310 =& 2\cdot3\cdot5\cdot7\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 1386, 924, 660, 495, 385, 308, 252 and 2310. )

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

$$\begin{aligned}1386 =& 2\cdot3\cdot3\cdot7\cdot11\\[8pt]924 =& 2\cdot2\cdot3\cdot7\cdot11\\[8pt]660 =& 2\cdot2\cdot3\cdot5\cdot11\\[8pt]495 =& 3\cdot3\cdot5\cdot11\\[8pt]385 =& 5\cdot7\cdot11\\[8pt]308 =& 2\cdot2\cdot7\cdot11\\[8pt]252 =& 2\cdot2\cdot3\cdot3\cdot7\\[8pt]2310 =& 2\cdot3\cdot5\cdot7\cdot11\\[8pt]\end{aligned}$$

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} } $.

GCD Calculator