Prime Factorization Calculator
Find prime factorization of any number.
Number Input
Enter a positive integer
Prime Factorization
Prime Factorization
60 = 2^2 × 3 × 5
Prime Factors
2, 2, 3, 5
Unique Primes
2, 3, 5
Expanded Form:
60 = 2 × 2 × 3 × 5
About This Calculator
The Prime Factorization Calculator finds the prime factorization of any number, expressing it as a product of prime numbers. According to the fundamental theorem of arithmetic, every composite number has a unique prime factorization.
Prime factorization is useful for finding the greatest common factor (GCF), least common multiple (LCM), simplifying fractions, and solving various number theory problems. The calculator shows both the expanded form and the exponential form of the prime factorization.
Formula & Calculation Method
Prime Factorization:
Method:
Divide by smallest prime (2, 3, 5, 7, ...)
Continue until result is prime
Example:
60 = 2 × 2 × 3 × 5
60 = 2² × 3 × 5
Fundamental Theorem of Arithmetic:
Every composite number has a unique prime factorization
Prime factorization breaks down a number into its prime components. Prime numbers are numbers greater than 1 that have exactly two factors: 1 and themselves. The factorization is unique for each number (ignoring the order of factors).
How to Use This Calculator
- Enter Number: Input the integer you want to factorize.
- View Results: See the prime factorization in both expanded and exponential form.
- Check Prime: See if the number itself is prime (cannot be factorized further).
- Use Factorization: Use prime factors to find GCF, LCM, or simplify calculations.
Frequently Asked Questions
What is prime factorization?
Prime factorization expresses a composite number as a product of prime numbers. For example, 12 = 2 × 2 × 3 = 2² × 3. Every composite number has a unique prime factorization (fundamental theorem of arithmetic).
Why is prime factorization unique?
The fundamental theorem of arithmetic states that every integer greater than 1 has a unique prime factorization (up to the order of factors). This means 12 can only be written as 2² × 3, not as any other combination of primes.
How do you find prime factorization?
Start with the smallest prime (2) and divide the number. If it divides evenly, record the prime and continue with the quotient. If not, try the next prime. Continue until the result is 1 or prime.
What is the use of prime factorization?
Prime factorization is used for: finding GCF and LCM, simplifying fractions, solving number theory problems, cryptography, and understanding the structure of numbers. It's a fundamental concept in mathematics.
Calculator by
NumCalculators Editorial Team
Multi-disciplinary Expert Team