gen-briefly-explain-the-fundamental-theorem-of-arithmetic-and-on-c99d

Briefly explain the fundamental theorem of arithmetic and one common misconception about it.

## Fundamental Theorem of Arithmetic The fundamental theorem of arithmetic states that **every integer greater than 1 can be expressed as a product of prime numbers in exactly one way** (ignoring the order of factors). For example: 60 = 2² × 3 × 5, and this is the *only* prime factorization of 60. ## Common Misconception Many people mistakenly think **the number 1 is prime** and should be included in prime factorizations. However, 1 is deliberately excluded from being prime precisely to preserve the "uniqueness" part of this theorem. If 1 were prime, then 60 could be written as 2² × 3 × 5, or 1 × 2² × 3 × 5, or 1² × 2² × 3 × 5, etc., destroying the unique factorization property that makes the theorem so powerful in mathematics.