Prime factorisation

Breaking a number into primes

Every whole number greater than one can be written as a product of primes, and in only one way. Enter a number and the tool factorises it, say 360 into 2³ × 3² × 5. It also lists every divisor and says whether the number is prime. Useful at school, and for cancelling fractions or finding common divisors.

How the factorisation works

The tool divides the number by the smallest primes in turn until it reaches one. How many times each prime divides it gives that prime's power in the result. The method is quick even for large numbers, because divisors only need testing up to the square root. It all runs in your browser.

Frequently asked questions

How large a number does it handle?

Up to one trillion. Beyond that, factorising in a browser would take too long.

What does it mean that a number is prime?

A prime is divisible only by one and by itself. In the factorisation it then appears alone, for example 97 = 97. The tool marks such numbers.

What is the list of divisors for?

It helps when you are looking for what divides a number exactly, say when simplifying fractions or splitting something into equal parts. We show every divisor from one up to the number itself.