Lenstra's algorithm is well suited for finding ``medium sized'' factors of an integer , which today means between to decimal digits. The ECM method is not directly used for factoring RSA challenge numbers (see Section 1.1.3), but it is used on auxiliary numbers as a crucial step in the ``number field sieve'', which is the best known algorithm for hunting for such factorizations. Also, implementation of ECM typically requires little memory. 
Lenstra
