Abstract: Shor's algorithm is an important quantum algorithm which has been commonly used as an example of how quantum computers can theoretically solve problems faster than classical computers. It has been shown to be theoretically able to solve the factoring of integers faster than the most efficient known classical algorithm. The problem of factoring numbers has important applications, such as in the field of online security. Starting from the basics of quantum computing, and using a quantum mechanical basis, we explain why Shor's algorithm is a uniquely quantum and more efficient solution to the factoring problem compared to any classical equivalent. Building on the quantum description, we show how two registers of qubits, which interfere with each other through entanglement, can be maninpulated through unitary transformations to evaluate a function. The period of the function can then be extracted using a quantum Fourier transform. In order to illustrate the algorithm using a concrete example, we examine results produced by an experimental quantum computer which was able to factor the number 15. We also show how the algorithm works by using classical calculations which imitate what we expect would happen in an ideal quantum system. This worksheet uses the Maple Quantum Chemistry Toolbox.