While exploring Brocard’s Equation , which is known to have 3 solutions, st. , we develop an algorithm to effectively store factorials of large numbers. First, we begin by prime-decomposing the factorial with the help of Legendre’s Formula. Then, we convert the resulting product of prime powers into a sum by taking logarithms of convenient base. Finally, we implement the algorithm to search for potential solutions in for Brocard’s Equation up to .