Cauchy’s Theorem is a fundamental result in group theory, a branch of mathematics. It states that if a finite group has a prime number p as a divisor of its order (the total number of elements in the group), then the group contains at least one subgroup of order p . This theorem is named after the French mathematician Augustin-Louis Cauchy. The significance of Cauchy’s Theorem lies in its application to the study of group structures. It helps mathematicians understand how groups can be broken down into smaller, simpler components, which is essential for analyzing their properties and behaviors in various mathematical contexts.