Is precomputation of the prime-factor-decomposition feasible?
Solution 1:
The problem is storage space. The total amount of harddrives ever produced by humanity can store around $10^{21}$ numbers.* But twenty-one-digit numbers are easy to factorise. So we could never store enough factorisations to make this plan worthwhile.
*For citation see here: https://www.zdnet.com/article/what-is-the-worlds-data-storage-capacity/ That's an old article, but it doesn't really matter. Thirty-digit numbers are also easy to factorise.