Decompose any positive integer into its prime factors, showing standard notation and prime power products.
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Prime factorization is the process of finding which prime numbers multiply together to make the original number. E.g. the prime factorization of **60** is \(2 \times 2 \times 3 \times 5\). In standard mathematical notations, this is written using exponent powers of prime bases: \(2^2 \times 3^1 \times 5^1\). According to the **Fundamental Theorem of Arithmetic**, every integer greater than 1 has a unique prime factorization. Finding prime factors is a crucial step in finding the GCD and LCM of numbers and is the foundation of modern cryptography.