Solve $371x\equiv 287\mod460$ using Chinese Remainder Theorem.
So far I've done $$460=4\times5\times23$$
Then the given congruence is equivalent to \begin{align*} 371x&\equiv287\mod4\\ 371x&\equiv287\mod5\\ 371x&\equiv287\mod23 \end{align*}
How to advance from here?
Use the extended Euclidean algorithm to obtain a Bézout's relation between $371$ and $460$: \begin{array}{r|rr|l} r_i&u_i&v_i&q_i\\ \hline 460&0&1\\ 371&1&0&1\\ 89&-1&1&4\\ 15&5&-4&5\\14&-26&21&1\\1&31&-25 \end{array} Thus a Bézout's relation is $$31\cdot 371-25\cdot460=1$$ so that the inverse of $371$ mod. $460$ is $31$, and the solutions are $$31\cdot 371 x\equiv x\equiv 31\cdot 287\equiv 157\mod 460.$$