What is prime factorization?

What is prime factorization?

• A. The expression of a number as a product of its prime factors
• B. The expression of a number as a sum of primes
• C. The expression of a number as a product of composite factors
• D. The expression of a number as a product of digits

Answer: (A)

Prime factorization is expressing a number as a product of prime numbers. It shows the building blocks of a number by breaking it down into primes that multiply together to give the original value, and the multiplicities of those primes are kept—the same primes can appear more than once. For example, 60 can be written as 2 × 2 × 3 × 5, where every factor is prime and their product equals 60. This is distinct from simply adding primes (which would be a sum, not a factorization), using a product of composite factors (which aren’t the prime building blocks), or multiplying digits (which isn’t related to factorization). The idea is to reveal the unique set of prime factors that compose the number.

Prime factorization is expressing a number as a product of prime numbers. It shows the building blocks of a number by breaking it down into primes that multiply together to give the original value, and the multiplicities of those primes are kept—the same primes can appear more than once. For example, 60 can be written as 2 × 2 × 3 × 5, where every factor is prime and their product equals 60. This is distinct from simply adding primes (which would be a sum, not a factorization), using a product of composite factors (which aren’t the prime building blocks), or multiplying digits (which isn’t related to factorization). The idea is to reveal the unique set of prime factors that compose the number.