Example 3 Find the greatest common divisor of $1008, 1260, 882$ and 1134.
Solve: Decompose these four numbers into prime factors
$$\begin{array}{l}
1008=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7=2^{4} \times 3^{2} \times 7 \\
1260=2 \times 2 \times 3 \times 3 \times 5 \times 7=2^{2} \times 3^{2} \times 5 \times 7 \\
882=2 \times 3^{2} \times 7^{2} \\
1134=2 \times 3^{4} \times 7
\end{array}$$

Therefore, $(1008,1260,882,1134)=2 \times 3^{2} \times 7=126$.