RSA encryption standard is a vital component of everyday internet communication. It is currently seen as being unbreakable as the problem that it is based on, semiprime factorisation, is an NP problem. Therefore, to try and break RSA using the current state of the art factoring method will take thousands of years. However, thanks to the advent of quantum computers we do know that RSA can theoretically be broken in seconds in two main ways. Firstly, by using Shor’s algorithm. Secondly, by formulating it as a binary optimisation problem and solving the formation with the quantum approximate optimization algorithm or solving the formulation by using quantum annealing. Unfortunately, there does not exist a quantum computer today that is accurate nor large enough to be able to break RSA encryption any time soon. For example, the largest semiprime number that has been factored by a quantum computer was a 41-bit number, as opposed to 2048-bit numbers that get used for RSA encryption. Fortunately, what is possible is to split the binary optimisation problem formulisation up into sub- problems, solve them individually and combine the solutions to get the answer, as shown in Wang et al. . Unfortunately, how the Wang et al. approach splits the problem up is not scalable, as when the problem gets larger so do the subproblems. Therefore, in the end the subproblems will expand to such a size that even they cannot be solved. The problem of ever expanding subproblems is the main focus of this thesis. We present a new approach that splits the problem into subproblems that are of constant size. Consequently, no matter how large the problem gets, all components can still be solved. Using our new method, we have been able to vastly outperform previous records set by quantum computers. However, our approach does not outperform current state of the art classical factoring methods. However, we also show that our new approach has limits. The increase in the amount of subprob- lems means an exponential increase in the spatial complexity when combining the solutions. Fortunately, we also present ways in which we can reduce the spatial complexity. These methods have a mixed success. However, they have meant that we can factor numbers that have more than triple the bit length than if we were not to use them. Finally, our techniques in reducing the spatial complexity have led us to discover a new weakness in RSA encryption. Therefore, potentially wreaking havoc on the security of the internet.