Prime Factor Calculator

What this calculator does

So, you want to know which prime numbers divide a given number. This tool lists them. Enter a positive integer greater than 1, and it returns the prime factors of that number, each one listed once.

If the number you enter is prime, the tool tells you so, since a prime number's only prime factor is itself.

How to use it

1. Enter a positive integer greater than 1.
2. Press Calculate.

What a prime factor is

A prime factor of a number is a prime that divides it evenly. Take 12: it is divisible by 2 and by 3, both of which are prime, so 2 and 3 are its prime factors. It is also divisible by 4 and 6, but those are not prime, so they do not count as prime factors. The tool checks each divisor of your number and keeps only the ones that are prime, giving you the primes that go into it.

The distinct primes, without repeats

The defining feature of this tool is that it lists each prime factor only once, however many times it actually divides the number. The number 12 is 2 times 2 times 3, so 2 divides it twice, but in this list 2 appears a single time: the prime factors are simply 2 and 3. The list answers the question "which primes divide this number?" rather than "how many times does each one divide?" It is the set of prime building blocks, stripped of their repetition, presented as a clean list separated by commas.

How it differs from prime factorization

This is the key thing that sets this tool apart from the prime factorization calculator, and it is easy to mix them up. Prime factorization gives the full product that rebuilds the number, with every prime repeated as often as it divides: 12 as 2 times 2 times 3. This tool gives only the distinct primes involved: 12 as 2 and 3. One is a multiplication that returns to your number; the other is a list of which primes take part. Reach for this tool when you want to know the primes present, and for the factorization tool when you want the exact product with all its repeats.

A worked example

Enter 60. Its divisors that happen to be prime are 2, 3, and 5, so the tool lists the prime factors of 60 as 2, 3, 5, each once, even though 2 actually divides 60 twice. Enter 13 instead, and since 13 is prime, the tool reports that 13 is a prime number, its only prime factor being itself.

Why the distinct primes matter

Knowing just the distinct primes of a number is often exactly what you need. When you are checking whether two numbers share any prime building blocks, it is the set of primes that matters, not how many times each appears. The distinct primes also tell you at a glance what kinds of factors a number has: a number whose only prime factor is 2 is a power of 2, and a number with a single prime factor is a prime power. This stripped-down view cuts straight to the primes involved.

Questions people ask

What is a prime factor?

A prime number that divides your number evenly. The prime factors of 12 are 2 and 3.

Why is each prime listed only once?

Because this tool gives the distinct primes that divide the number, not how many times each divides. So 12 gives 2 and 3, not 2, 2, 3.

How is this different from prime factorization?

Prime factorization gives the full product with repeats, like 2 times 2 times 3. This tool gives only the distinct primes, like 2 and 3.

What if my number is prime?

Then its only prime factor is itself, and the tool tells you the number is prime.

Why aren't 4 and 6 prime factors of 12?

Because they are not prime. Only prime divisors count as prime factors, so 4 and 6 are left out.

References

On distinct prime factors. The distinct prime factors of a number are the different primes that divide it, listed without repetition.

1. Eric W. Weisstein, "Distinct Prime Factors," from MathWorld, a Wolfram resource, on the distinct primes appearing in a number's factorization.
2. Eric W. Weisstein, "Prime Factor," from MathWorld, a Wolfram resource, on the prime factors of an integer.