Prime Factorization Calculator
Decompose any composite number into its prime factors instantly. Generate a factor tree, find all divisors, and check if a number is prime.
What is Prime Factorization?
Prime Factorization is the process of breaking down a composite number into a product of prime numbers. Every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers in a unique way (The Fundamental Theorem of Arithmetic).
For example, the number 12 can be written as:
12 = 2 × 2 × 3 = 2² × 3
Why is this useful?
- Cryptography: Large prime numbers are the foundation of modern encryption (RSA) used to secure the internet.
- Simplifying Fractions: Breaking numerator and denominator into primes makes it easy to cancel out common factors.
- Finding LCM and GCF: Prime factorization is the most reliable method for finding the Least Common Multiple and Greatest Common Factor of two or more numbers.
? Frequently Asked Questions
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself (e.g., 2, 3, 5, 7, 11).
No. By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor, so it is not prime.
You can use a Factor Tree. Start by dividing the number by the smallest prime (2). If it divides evenly, branch out. Continue dividing the results by the smallest possible primes until all branches end in prime numbers.