Integers factorization is one of the fundamental problems in number theory and cryptography of public key. One of the oldest and most renowned methods in this field is Fermat's factorization algorithm, but its performance decreases sharply for large values of n, which are the product of two distant prime numbers. In the present study, Horváth's Phi Factorization and its optimized version, that is Phi2 Factorization, is compared with Fermat and Second Fermat methods. Phi and Phi2 by exploiting optimized calculations and special relations in the number theory are more efficient than the Fermat method in many cases. In this study, first, the quad algorithms were investigated and implemented and then experimentally analyzed on different numbers. Findings showed that Horváth's proposed methods compared to Fermat methods have fewer computational operations compared to Fermat methods and perform more efficiently at execution time. In addition, to show the superiority of the proposed methods, detailed evaluations based on the number of comparisons, sums, and bit-shifts are presented, and analytical graphs and tables confirm the results. Finally, the advantages and disadvantages of each method were examined, and suggestions were presented to improve the performance of the algorithm factorization in cryptography issues.