If $x_i$ is an integer greater than 1, let $f(x_i)$ be the greatest prime factor of $x_i,x_{i+1} =x_i-f(x_i)$ ($i\ge 0$ and i is an integer). (1) Prove that for any integer $x_0$ greater than 1, there exists a natural number$k(x_0)$, such that $x_{k(x_0)+1}=0$ Grade 10: (2) Let $V_{(x_0)}$ be the number of different numbers in $f(x_0),f(x_1),\cdots,f(x_{k(x_0)})$. Find the largest number in $V(2),V(3),\cdots,V(781)$ and give reasons. Note: Bai Lu Zhou Academy was founded in 1241 and has a history of 781 years. Grade 11: (2) Let $V_{(x_0)}$ be the number of different numbers in $f(x_0),f(x_1),\cdots,f(x_{k(x_0)})$. Find the largest number in $V(2),V(3),\cdots,V(2022)$ and give reasons.