Factoring large numbers I am trying to factor few integers that are each between 115 and 135 digits long. I was wondering if anyone knew of any efficient methods or any programs that I could use to find the two primes $p$ and $q$ for $n=pq$.

I was thinking of using quadratic sieve but I don't know if there is any other way. Plus I don't know how I would write the algorithm on any program. Any input is much appreciated.
As for the algorithm, you have two choices: The quadratic sieve and the general number field sieve.

If you want to implement the factorization yourself you want to use the quadratic sieve, as a good implementation of the GNFS is really hard.

However, if you're willing to use pre-made tools using GGNFS and msieve (together) is your best option. Msieve provides good polynomial selection (first step) and GGNFS provides the efficient second step, while msieve takes over the last step, you may want to refer to this guide for the exact how-to.