In the prime factorization of a composite number, the only factors included are prime numbers. By definition, a composite number is a whole number greater than one that is not prime, meaning it has more than two distinct positive divisors: 1 and itself.
For example, let’s take the composite number 12. The prime factorization of 12 is 2 × 2 × 3 or more succinctly, 22 × 3. In this case, the factors 1 and 12 are not included in the prime factorization. This is because prime factorization is concerned only with prime numbers that multiply together to achieve the composite number.
Similarly, when we factor composite numbers, we avoid including any composite numbers or the number 1 in the representation since they do not fulfill the criteria of prime numbers. Thus, the factors that are explicitly excluded from prime factorization include:
- 1
- Any composite numbers (like 4, 6, 8, etc.)
In summary, only prime numbers are included in the prime factorization, while 1 and composite numbers are not.