Jasper Yu says to YSITD
RSA, a most commonly used asymmetric cryptography algorithm for encrypting message. Usually RSA is unbreakable, but there are some situation that can cause the algorithm to be vulnerable. One case is when some keys shared their prime, which makes the process of cracking keys relatively easy. In order to find the common factor of two key pairs, we can use the Euclidean algorithm for calculating the common factor for huge numbers.