Computing the LZ factorization (or LZ77 parsing) of a string is a computational bottleneck in many diverse applications, including data compression, text indexing, and pattern discovery. We describe new linear time LZ factorization algorithms, some of which require only 2nlogn + O(logn) bits of working space to factorize a string of length n. These are the most space efficient linear time algorithms to date, using n logn bits less space than any previous linear time algorithm. The algorithms are also simple to implement, very fast in practice, and amenable to streaming implementation.