Factor calculator
All the factors of a number, its factor pairs and its prime factorization.
About this calculator
This factor calculator lists every factor of a whole number, the numbers that divide it with no remainder, along with its factor pairs.
It also gives the prime factorization and tells you whether the number is prime, perfect, abundant or deficient.
How it works
A factor divides the number with no remainder. Testing every whole number up to the square root finds each small factor, and dividing the number by it gives its pair. A perfect number equals the sum of its other factors.
Last reviewed:
Worked example
- Whole number: 360
Number of factors: 24 (An abundant number)
Common questions
What are the factors of 24?
1, 2, 3, 4, 6, 8, 12 and 24. They come in pairs that multiply to 24: 1 × 24, 2 × 12, 3 × 8 and 4 × 6.
What is the difference between factors and multiples?
Factors divide into a number, while multiples are what you get when you multiply it. 3 is a factor of 12, and 12 is a multiple of 3.
How do I know if a number is prime?
A prime has exactly two factors, 1 and itself. Enter it here: if the calculator finds only two factors, it's prime.
Sources and further reading
The story behind it
Where the idea came from: Around 300 BC, Euclid showed that 2ⁿ⁻¹(2ⁿ − 1) is a perfect number whenever 2ⁿ − 1 is prime.
Perfect numbers such as 6, 28 and 496 equal the sum of their other factors. Only a few dozen are known, and every one found so far is even.
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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