Integer factorization is one of the vital algorithms discussed as a part of analysis of any black-box cipher suites where the cipher algorithm is based on number theory. The origin of the problem is from Discrete Logarithmic Problem which appears under the analysis of the crypto-graphic algorithms as seen by a crypt-analyst. The integer factorization algorithm poses a potential in computational science too, obtaining the factors of a very large number is challenging with a limited computing infrastructure. This paper analyses the Pollards Rho heuristic with a varying input size to evaluate the performance under a multi-core environment and also to estimate the threshold for each computing infrastructure.