Prime factorization calculator
The prime factors of a number, its divisors, and whether it is prime.
About this calculator
This prime factorization calculator breaks a number into the primes that multiply to make it, such as 360 = 2³ × 3² × 5.
It also tells you whether the number is prime, and lists its divisors and their sum.
How it works
Divides by each prime in turn, starting from 2, as many times as it goes in, until what is left is 1 or a prime. The divisors are every product of those prime factors.
Last reviewed:
Worked example
- Whole number: 360
Prime factorization: 2³ × 3² × 5 (a composite number)
Common questions
What is a prime number?
A whole number above 1 whose only divisors are 1 and itself, such as 2, 3, 5, 7 and 11. 1 is not prime.
Why is prime factorization useful?
It makes it easy to find the GCF and LCM, simplify fractions and square roots, and it is the basis of modern cryptography.
How many divisors does a number have?
Add 1 to each exponent in its prime factorization and multiply. 360 = 2³ × 3² × 5 has 4 × 3 × 2 = 24 divisors.
The story behind it
Where the idea came from: Euclid proved around 300 BC that there are infinitely many prime numbers.
Every whole number above 1 breaks into primes in exactly one way, a result known as the fundamental theorem of arithmetic. Splitting very large numbers into primes is so hard that the security of online banking relies on it.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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