Breaks any whole number down into the prime numbers that multiply together to make it.
How it works
The number is repeatedly divided by the smallest possible prime until only primes remain, using trial division.
What this does not include
This does not include finding all divisors of a number (not just prime ones) — this calculator specifically returns the prime factorization.
How to use this calculator
- Enter a whole number of 2 or greater.
A worked example
84 → repeatedly dividing by the smallest possible prime: 84 = 2 × 2 × 3 × 7, so the prime factorization is 2² × 3 × 7.
60 → 2² × 3 × 5.
What the process does
| Step | What happens |
|---|---|
| Trial division | Divide by the smallest possible prime repeatedly until it no longer divides evenly |
| Move to next prime | Once a prime stops dividing evenly, try the next one up |
| Stop | When only 1 remains, every prime factor has been found |
Edge cases worth knowing
A prime number’s factorization is just itself — there’s nothing smaller to divide it by, since primes by definition have no factors besides 1 and themselves.
Every whole number greater than 1 has exactly one prime factorization — a foundational result in number theory known as the fundamental theorem of arithmetic.
Frequently asked questions
What makes a number prime?
A prime number has exactly two factors: 1 and itself. Every other whole number greater than 1 can be broken down into a unique product of primes.
Why is prime factorization useful?
It’s the foundation of number theory topics like finding greatest common divisors, least common multiples, and simplifying fractions.
What if I enter a prime number?
The result is simply that number itself, since a prime has no smaller prime factors to break it down further.
