8. Find the greatest common divisor using the method of prime factorization:
(i) $48,84,120$.
(ii) $360,810,1260,3150$.
8.
(i) Solution: Decomposing each number into prime factors, we get
$$\begin{array}{l}
48=2 \times 2 \times 2 \times 2 \times 3=2^{4} \times 3 \\
84=2 \times 2 \times 3 \times 7=2^{2} \times 3 \times 7 \\
120=2 \times 2 \times 2 \times 3 \times 5=2^{3} \times 3 \times 5
\end{array}$$

Therefore, $(48,84,120)=2^{2} \times 3=12$.
(ii) Solution: Decomposing each number into prime factors, we get
$$\begin{array}{l}
360=2^{3} \times 3^{2} \times 5 \\
810=2 \times 3^{4} \times 5 \\
1260=2^{2} \times 3^{2} \times 5 \times 7 \\
3150=2 \times 3^{2} \times 5^{2} \times 7
\end{array}$$

Therefore, $(360,810,1260,3150)=2 \times 3^{2} \times 5=90$.