How are composite numbers typically expressed using prime factors?

• A. As a sum of prime factors
• B. As a single prime factor
• C. As a product of composite factors
• D. As a product of prime factors with exponents

Answer: (D)

Prime factorization shows exactly which prime numbers multiply to make a composite number and how many times each prime is used. Writing a number as a product of prime factors with exponents gives the shortest, most complete description of its building blocks.

For example, 360 can be written as 2^3 × 3^2 × 5. This tells us the number is built by multiplying three 2s, two 3s, and one 5. The exponents show how many times each prime appears, which is what makes this representation precise and unique (up to the order of factors).

It isn’t a sum, because multiplying primes builds the number, not adding them. It isn’t just a single prime factor, since a composite number has more than one prime factor. And it isn’t a product of composite factors if we want the simplest, most informative form, because that would hide the prime building blocks. So expressing a composite number as a product of prime factors with exponents is the standard, most informative way.