Prime Factorization Calculator
Break a number down into its prime factors.
A number's prime building blocks
Every whole number greater than one can be written as a product of prime numbers, and that breakdown is unique to it. This finds the prime factorisation of a number, showing the primes that multiply together to make it.
Enter a number to find its prime factors.
Why the prime factorisation is so useful
The prime factorisation is a number's fingerprint — the fundamental theorem of arithmetic guarantees every number has exactly one, which is why primes are the building blocks of arithmetic. It is genuinely practical too: once you have the prime factors of two numbers, their greatest common divisor and least common multiple fall right out, which is what you need for simplifying and adding fractions. It also reveals all the factors of a number, and whether it is a perfect square or has other special structure. Factoring gets hard for very large numbers, a difficulty that, as with primality, underpins modern encryption. For everyday numbers, the factorisation is a compact summary of everything about how a number is built.
Frequently asked questions
What is prime factorisation?
Writing a number as a product of prime numbers — its unique set of prime building blocks, guaranteed by the fundamental theorem of arithmetic.
What is it useful for?
Finding the greatest common divisor and least common multiple of numbers, simplifying and adding fractions, and revealing a number's structure.
Is anything uploaded?
No. The calculation happens in your browser.