In prime factorization, the final result consists only of what type of numbers?

• A. Whole Numbers
• B. Composite Numbers
• C. Integers
• D. Prime Numbers

Answer: (D)

In prime factorization, the final result consists solely of prime numbers. This is because prime factorization involves breaking down a composite number into a product of its prime factors. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, meaning it has exactly two distinct positive divisors: 1 and itself.

When you perform prime factorization, you continuously divide the original number by the smallest possible prime numbers until you reach 1, resulting only in a multiplication of prime numbers. For example, if you take the composite number 60, its prime factorization would be (2 \times 2 \times 3 \times 5) or (2^2 \times 3 \times 5). Each of the factors in this final expression is a prime number (2, 3, and 5).

Recognizing that the result of the factorization is exclusively made up of prime components is crucial when working with numbers in this way. Other types of numbers, such as composite numbers, whole numbers, or integers, may be involved in the process initially, but the essence of prime factorization is that it distills numbers down to their irreducible prime factors