Prime Factorization Calculator Formula & How It Works
n = p₁^a₁ × p₂^a₂ × p₃^a₃ × … (Fundamental Theorem of Arithmetic)
- Every integer > 1 is either prime or can be written as a unique product of primes
- Trial division: divide by 2, then 3, 5, 7, 11 … up to √n
- Continue until quotient is 1
- Result: list each prime factor with its exponent
The Fundamental Theorem of Arithmetic states that every integer > 1 has a unique prime factorization. Find it by trial division: divide repeatedly by the smallest prime that goes in evenly (2, then 3, 5, 7, …). Example: 360 = 2³ × 3² × 5. Used in GCF, LCM, and number theory.