About Factors of a Number Calculator
This factors of a number calculator lists every number that divides yours exactly, together with the count of divisors, their sum and the prime factorization behind them. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 720 = 2^4 × 3^2 × 5. It has 30 factors, from 1 to 720, and they add up to 2418. The count comes straight from the exponents: (4 + 1)(2 + 1)(1 + 1) = 30.
Compare 36 = 2^2 × 3^2, which has 9 factors. The count is odd because 36 is a perfect square: the factors pair up as 1 × 36, 2 × 18, 3 × 12, 4 × 9 and the middle one, 6, pairs with itself.
How to use Factors of a Number Calculator
- Choose Factorization, Factor tree, Is it prime or Divisors.
- Type a whole number of 2 or more. Up to 24 digits are accepted.
- Read the prime factorization in exponent form at the top.
- Look at the factor tree, the list of divisors and their count and sum underneath.
- Open the steps to see the repeated division that produced each prime.
Features
- Prime factorization in exponent form and as a plain product.
- Factor tree drawn as a scalable diagram, with the primes filled in.
- Is-it-prime check with the smallest factor when the number is composite.
- Every divisor listed, plus the count and the sum of divisors.
- Numbers of up to 24 digits using exact big-integer arithmetic.
- Trial division for small numbers and Pollard rho for large ones.
- Repeated-division steps in KaTeX.
Counting and adding factors
Use the exponents of the prime factorization.
720 = 2⁴ × 3² × 5
count = (4 + 1)(2 + 1)(1 + 1) = 30
sum = (2⁵ - 1)/(2 - 1) × (3³ - 1)/(3 - 1) × (5² - 1)/(5 - 1) = 31 × 13 × 6 = 2418Worked examples
Factors of 720 gives 30 factors, sum 2418
Includes 1 and 720.
Factors of 36 gives 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
An odd count because 36 is a perfect square.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The number you enter is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To test a number by hand, try dividing by primes up to its square root. If none divides it, it is prime.
- 1 is not prime and not composite. 2 is the only even prime.
- A number with an odd count of divisors is a perfect square.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I find all the factors of a number?
Test every whole number up to its square root and pair each divisor with its partner. Or take its prime factorization and multiply the prime powers in every combination.
How many factors does a prime number have?
Exactly two: 1 and itself.