Prime Factorization of 120

Write the prime factorization of 120.

Prime factorization is a foundational concept in number theory, which involves expressing a number as a product of its prime numbers. Prime numbers are those greater than 1 that have no divisors other than 1 and themselves. The process of finding prime factors involves checking for divisibility starting from the smallest prime number, 2, and continuing with larger primes, such as 3, 5, 7, and so forth, until the quotient is a prime number. Knowledge of divisibility rules can greatly enhance this process, such as even numbers being divisible by 2, or numbers whose digits sum to a multiple of 3 being divisible by 3.

Understanding prime factorization is crucial for various areas of mathematics including simplifying fractions, finding least common multiples, and solving problems related to divisors. Moreover, recognizing the unique factorization theorem, or the fundamental theorem of arithmetic, which states that every integer greater than 1 has a unique prime factorization, underscores the significance of this concept in mathematical problem solving and theory development. In computer science, this concept also finds applications in algorithms, cryptography, and system optimization strategies, making it an integral part of discrete mathematics. By mastering prime factorization, students can develop a stronger foundation for advanced studies and practical applications in computer science and mathematics.