The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be uniquely represented as a product of prime numbers. This means that every number has a unique prime factorization. For example, the number 12 can be written as 2 x 2 x 3. This theorem is crucial in number theory as it helps us understand the relationship between prime numbers and composite numbers. It also allows us to simplify calculations involving factors and multiples. To prove the Fundamental Theorem of Arithmetic, we start by assuming that there exists a number that cannot be expressed as a product of prime numbers. By using the method of contradiction, we can show that this assumption leads to a contradiction and therefore must be false. Understanding this theorem not only deepens our understanding of the properties of numbers but also allows us to solve problems involving factorization and divisibility more efficiently. It is a foundational concept in mathematics that underpins many other mathematical principles.