About Prime Factorization
Prime factorization is the process of decomposing a number into a product of prime numbers.
Every positive integer has a unique prime factorization (Fundamental Theorem of Arithmetic).
Examples:
- 12 = 2² × 3
- 100 = 2² × 5²
- 2024 = 2³ × 11 × 23
Properties:
- Every integer greater than 1 can be uniquely factored into primes
- The order of the prime factors doesn't matter
- Prime numbers have exactly one prime factor (themselves)
- 1 has no prime factors
Applications:
- Number theory
- Cryptography
- Finding greatest common divisors
- Simplifying fractions