Prime Factorization of 280

Write the prime factorization of 280.

Prime factorization involves expressing a number as a product of prime numbers, which are numbers greater than one that have no divisors other than one and themselves. In this problem, you are tasked with finding the prime factorization of 280. This involves determining which prime numbers can be multiplied together to yield the original number, 280. The process typically starts with dividing the number by the smallest prime, which is two, and continuing the division with subsequent primes like three, five, seven, and so on, until the number is fully resolved into a product of primes.

Understanding prime factorization is crucial in number theory due to its role in simplifying fractions, computing greatest common divisors, and solving problems related to divisibility and modular arithmetic. This fundamental concept helps in decomposing problems into simpler, manageable parts and is a building block for more advanced topics like cryptography, where large prime factorizations are used in securing information.

As you work through prime factorization, think about the efficiency of your process and how prime factorization algorithms, such as the trial division or the Sieve of Eratosthenes, provide systematic ways to find prime numbers and their products. Consider how breaking down numbers into their prime components can lead to more insight into their properties and relationships with other numbers.