Prime Factorization Calculator
Prime factorization expresses a number as a product of prime numbers. Every integer > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). Example: 360 = 2^3 x 3^2 x 5. The trial division algorithm divides by each prime in sequence. Use prime factorization to find GCF (Greatest Common Factor) by taking minimum exponents, and LCM (Least Common Multiple) by taking maximum exponents of shared primes.
Find the prime factorization of any number up to 10,000,000. Shows prime factors with exponents, all divisors, and checks if the number is prime. Also calculates GCF (Greatest Common Factor) and LCM (Least Common Multiple) for two numbers.
Mode
Quick Examples
Enter a Number
How to Use
- 1
Enter a number
Type any integer from 1 to 10,000,000 in the input field. Or click one of the Quick Examples (12, 360, 1024, 997, 9999) to see a demonstration.
- 2
View the factorization
The result shows the prime factorization in canonical form with exponents (e.g. 360 = 2^3 x 3^2 x 5) and the full expansion (2 x 2 x 2 x 3 x 3 x 5). If the number is prime, a green badge indicates it.
- 3
Check all divisors
Scroll down to see every whole number that divides evenly into the result. The count shows how many divisors the number has (perfect squares have an odd number of divisors).
- 4
Calculate GCF and LCM
Switch to GCF & LCM mode to enter two numbers. The calculator shows the factorization of both and computes the Greatest Common Factor and Least Common Multiple simultaneously.