# Factorization of the public value $N$ from the RSA cryptosystem

It is mentioned here that the public value $$N=p*q$$ of the RSA cryptosystem can be factorized if one of the factors is reused. Thus, if $$N_1=p*q_1$$ and $$N_2=p*q_2$$ and only $$N_1$$ and $$N_2$$ are known, then one can factor $$N_1$$ and $$N_2$$.

I wasn't able to come up how this can be achieved. Is that statement really true?

Since $$p$$ is a factor in both $$N_1$$ and $$N_2$$ you can simply calculate $$p$$ by using Euclid's algorithm.
Once you have $$p$$ you can then calculate $$q_1$$ and $$q_2$$ (simply divide $$N_1$$ by $$p$$ to get $$q_1$$ and divide $$N_2$$ by $$p$$ to get $$q_2$$).