Fermat's Factorization is a method for finding the prime factors of a composite number. It is based on the idea that any odd integer can be expressed as the difference of two squares. By representing a number n as n = a^2 - b^2 , where a and b are integers, we can factor n into (a-b)(a+b) . To apply this method, one starts with an integer a that is the smallest integer greater than the square root of n . Then, b^2 is calculated as a^2 - n . If b^2 is a perfect square, the factors can be easily found. If not, a is incremented, and the process is repeated until a solution is found.