What is the fundamental theorem of arithmetic?

The fundamental theorem of arithmetic states that every integer greater than 1 is either prime or can be uniquely factored into prime numbers (ignoring order). This makes prime factorization unique for each number.

How do I use prime factorization to find GCD?

Find the prime factorization of each number, then multiply the common prime factors (using the lowest power of each). For example, GCD(12,18): 12=2²×3, 18=2×3², so GCD=2×3=6.

What if a number is already prime?

If a number is prime, its only prime factor is itself. The calculator will show that the number is prime and cannot be factored further.

How large a number can I factor?

The calculator can handle reasonably large numbers, but factoring very large numbers (hundreds of digits) can be extremely time-consuming. This difficulty is actually the basis for RSA encryption security.

Prime Factorization Calculator – Factor into Primes

Find the prime factorization of any number. Break down composite numbers into their prime factors with complete factor trees.

Prime Factorization Calculator – Factor into Primes

Find the prime factorization of any number. Break down composite numbers into their prime factors with complete factor trees.

Number*

Enter a number to factor (must be 2 or greater)

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Understanding Prime Factorization

Prime factorization breaks down a composite number into a product of prime numbers. Every integer greater than 1 has a unique prime factorization, which is fundamental to number theory and has many practical applications.

Applications of Prime Factorization

Prime factorization is used in:

Finding GCD and LCM of numbers
Simplifying fractions and radicals
Cryptography and computer security
Number theory research
Algorithm optimization
Mathematical proofs and analysis

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your number
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

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