What does the prime factorization of a number help to determine?

The prime factorization of a number helps to determine whether the number is prime or composite by expressing the number as a product of its prime factors. A prime number has exactly two distinct positive divisors: 1 and itself, meaning that its prime factorization consists of just the number itself. In contrast, a composite number has more than two positive divisors and can be broken down into two or more factors that are prime numbers. By identifying the prime factorization, one can easily conclude if the number can be divided by any primes other than 1 and itself, thereby establishing its composites status.

The other options do not accurately represent what the prime factorization reveals about a number. For example, it does not indicate the number of digits in a number, as numbers can have varying digit lengths irrespective of their prime factors. Additionally, prime factorization does not provide information about the size of the number directly, since larger composite numbers can have simpler prime factorizations than smaller numbers. Lastly, while prime factorization can relate to multiples, it does not directly determine what multiples exist; it focuses primarily on the atomic building blocks of the number rather than its multiples in the broader numerical system.