Sieve of Eratosthenes is a way to compute prime factors of a number by pre-computing the smallest prime-factors of all numbers till a limit.
A great video tutorial by Khan Academy -
Also I recommend you to read this blog on CodeForces - Prime Factorization In log(n) After Sieves
All these algorithms take O(n log n) time. This can be also done in time O(n). See here - Sieve of Eratosthenes in 0(n) time complexity