This study delves into the realms of number theory, specifically investigating perfect numbers and partitions of odd numbers. Perfect numbers, which are integers equal to the sum of their proper divisors, excluding themselves, have intrigued mathematicians for centuries. While it is established that even perfect numbers can be expressed as 2p-1(2p -1) , where 𝑝 and 2p -1 are prime numbers (Mersenne primes), the existence of odd perfect numbers remains an unsolved problem. The first part of the thesis explores perfect numbers, tracing their history from ancient Greek mathematicians to modern scholars, and discussing various results and conjectures. The focus then shifts to partitions of odd numbers, which represent different ways of expressing an odd number as a sum of positive integers. The study utilizes an algorithms that has demonstrated that a positive even integer can be partitioned into all pairs of odd numbers. Using this approach, it is shown that any positive odd number 2𝑛 + 1 can be partitioned into all pairs of both odd and even numbers and from the set of these partitions, it is shown that there exist a proper subset containing all proper divisors of 2𝑛 + 1. Using the results from the partitions and the facts that there exist infinitely many odd numbers, it’s therefore verifies that odd perfect numbers do not exist.