What is the Prime Factorization Calculator?
Prime factorization writes a number as a product of prime numbers. Every whole number above 1 has exactly one such representation, which is why primes are called the building blocks of numbers.
How to use the Prime Factorization tool
- Enter Number.
- The result updates instantly as you type, or press Calculate.
- Use Try an example to see how it works, and Reset to start again.
Formula
Divide repeatedly by the smallest prime that fits (2, 3, 5, 7, …) until the quotient is 1.
Worked example
With number 360, the prime factorization comes to 2^3 × 3^2 × 5. Is prime: No.
Frequently asked questions
What is prime factorization used for?
It finds GCF and LCM, simplifies fractions and underpins encryption.
Is the factorization unique?
Yes. This is the fundamental theorem of arithmetic.
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Checked by Calcovate · Formula tested against worked examples · Updated 7 Nov 2026 · How we check our calculators.