What is the prime factorization of 60?

Prime factorization expresses a number as a product of prime numbers. Process: divide by smallest primes repeatedly. 60 ÷ 2 = 30; 30 ÷ 2 = 15; 15 ÷ 3 = 5; 5 ÷ 5 = 1. So 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. Primes are natural numbers > 1 divisible only by 1 and themselves: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37... Composite numbers are non-prime natural numbers > 1; they can be factored into primes. 1 is neither prime nor composite. 2 is the only even prime. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic). Uses of prime factorization: (1) Finding GCF (greatest common factor) — multiply common prime factors with smallest exponents; (2) Finding LCM (least common multiple) — multiply all prime factors with largest exponents; (3) Simplifying fractions and radicals; (4) Number theory problems. Example: GCF of 60 and 84: 60 = 2²·3·5, 84 = 2²·3·7; common factors: 2², 3; GCF = 4·3 = 12.