gen-briefly-explain-prime-factorization-and-one-common-misconcep-2253

Briefly explain prime factorization and one common misconception about it.

## Prime Factorization **Prime factorization** is the process of breaking down a composite number into a product of prime numbers. Every composite number can be expressed as a unique combination of prime factors (this is called the Fundamental Theorem of Arithmetic). **Example:** 24 = 2 × 2 × 2 × 3 = 2³ × 3 ## Common Misconception **"1 is a prime number"** — Many people mistakenly believe 1 is prime, but by definition, prime numbers must have exactly two distinct factors (1 and itself). Since 1 only has one factor (itself), it is neither prime nor composite. Excluding 1 from the primes also preserves the uniqueness of prime factorization—if 1 were prime, we could write 24 = 2³ × 3 × 1 × 1 × 1... infinitely many ways.