Which statement is NOT a property of prime factorization?

• A. Every composite number can be written as a product of primes
• B. Exponents can show repeated primes
• C. The order of factors does not affect the product
• D. It always yields a single prime factor

Answer: (D)

Prime factorization writes a number as a product of prime numbers, using exponents to show how many times a prime appears. For any composite number, you can break it down into primes, and the order of multiplying those primes doesn’t matter because multiplication is commutative. Exponents are handy because they compactly show repeated primes, like 60 = 2^2 × 3 × 5 or 18 = 2 × 3^2.

The statement that always yields a single prime factor isn’t true for composites. Most numbers have several prime factors in their factorization (for example, 18 has 2 and 3, with 3 appearing twice). Only a prime number itself has effectively a single prime factor.