In the following exercises, find the prime factorization....

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Key Concepts

Prime Factorization

Prime factorization is the process of breaking down a composite number into the product of its prime components. This method is essential in number theory and helps reveal the basic building blocks of numbers, which can simplify computations and provide insights into number properties.

Prime Numbers

Prime numbers are numbers greater than 1 that are divisible only by 1 and themselves. They are fundamental to arithmetic because they serve as the building blocks for all natural numbers, underpinning the structure of number systems and playing a critical role in various branches of mathematics.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely expressed as a product of prime numbers, disregarding the order of multiplication. This theorem establishes that prime factorization is a unique representation for every number, which is essential for understanding the properties and relationships within the set of natural numbers.

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