Prime Factorization Calculator
Find prime factors of a number
Frequently Asked Questions
What is prime factorization?
Prime factorization breaks a number into its prime factors. For example, 360 = 2³ × 3² × 5. Every integer greater than 1 has a unique prime factorization (fundamental theorem of arithmetic). The calculator shows the complete factorization.
How is prime factorization performed?
Divide by the smallest prime (2) repeatedly, then try 3, 5, 7, and so on. For 180: 180/2=90, 90/2=45, 45/3=15, 15/3=5, 5/5=1. Result: 180 = 2² × 3² × 5. The calculator shows each step.
How is prime factorization used to find GCD and LCM?
GCD: take the minimum power of each common prime. LCM: take the maximum power of each prime. For 12=2²×3 and 18=2×3²: GCD = 2¹×3¹ = 6, LCM = 2²×3² = 36.
What are the practical applications of prime factorization?
Simplifying fractions, finding GCD/LCM, cryptography (RSA), determining the number of divisors (multiply exponents+1: 360 has (3+1)(2+1)(1+1) = 24 divisors), and solving number theory problems.
How many divisors does a number have?
From the prime factorization n = p₁^a₁ × p₂^a₂ × ..., the number of divisors is (a₁+1)(a₂+1)... For 360 = 2³×3²×5¹: divisors = (3+1)(2+1)(1+1) = 24. The calculator lists all divisors.