8. The number $\left(2^{222}\right)^{5} \times\left(5^{555}\right)^{2}$ is $Q$ digits long. What is the largest prime factor of $Q$ ?
SolUtion
101

The number $\left(2^{222}\right)^{5} \times\left(5^{555}\right)^{2}=2^{1110} \times 5^{1110}=10^{1110}$.
The number $10^{1110}$ is 1111 digits long, so $Q=1111=11 \times 101$.
Both 11 and 101 are prime.
Hence the largest prime factor of 1111 is 101 .