About Factor Tree Calculator
This factor tree calculator splits a number into smaller and smaller factors until every branch ends in a prime, and draws the tree for you. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 360. The tree splits off the smallest prime at each level: 360 = 2 × 180, 180 = 2 × 90, 90 = 2 × 45, 45 = 3 × 15, 15 = 3 × 5. The primes at the ends of the branches, 2, 2, 2, 3, 3, 5, are the prime factorization, 2^3 × 3^2 × 5.
Different splits give different looking trees, such as 360 = 20 × 18 first, but every tree ends in the same primes. That is the unique factorization theorem. The calculator always splits off the smallest prime so the picture is neat and the same each time.
How to use Factor Tree 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.
Reading a factor tree
Multiply the primes at the ends of the branches to get the number back.
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5Worked examples
Factor tree of 360 gives 2^3 × 3^2 × 5
Six prime leaves counting repeats.
Factor tree of 84 gives 2^2 × 3 × 7
84 = 2 × 42, 42 = 2 × 21, 21 = 3 × 7.
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 draw a factor tree?
Write the number at the top, split it into two factors, and repeat on each factor that is not prime. Circle the primes. The circled primes are the factorization.
Does it matter how I split the number?
No. Any split ends in the same primes. Only the shape of the tree changes.
More Prime Factorization Calculator pages
- Prime Factorization CalculatorEnter a whole number to get its prime factors in exponent form, a factor tree and every divisor.
- Is It Prime? Prime Number CheckerEnter a number to find out whether it is prime.
- Factors of a Number CalculatorEnter a number to list all its factors, how many there are, and what they add up to.