Prime Factorization Calculator

Break a whole number into its prime factors, shown both as a factor tree and in exponent form like 60 = 2² × 3 × 5. Enter the number and read the breakdown instantly. A free prime factorization calculator that runs in your browser, with no sign-up.

  • Exact, step-by-step answers
  • 100% free
  • No sign-up, no app
  • Instant as you type
  • Works offline after first load
Prime factorization of 60
2² × 3 × 5
60 = 2 × 2 × 3 × 5
Factor tree
  1. 60=2×30
  2. 30=2×15
  3. 15=3×5
  4. 5=5×1

How to use it

  1. 1

    Enter a whole number

    Type the number you want to factor. It should be a positive integer greater than one.

  2. 2

    Read the prime factors

    See the list of prime factors and the tidy exponent form, such as 2² × 3 × 5.

  3. 3

    Follow the tree

    The factor tree shows how the number splits step by step, which makes the result easy to check.

When it comes in handy

Simplifying fractions

Prime factors of the top and bottom reveal the common factors to cancel, reducing a fraction to lowest terms.

Finding LCM and GCD

Comparing the prime factorizations of two numbers is a clean way to read off their lowest common multiple and greatest common divisor.

Number theory homework

Check a factorization quickly, with both the tree and the exponent form shown so the steps are clear.

Instant, exact & 100% in your browser

The maths runs right here in your browser, with fractions and whole numbers kept exact rather than rounded along the way. Nothing you type is sent to a server, there is no sign-up and no limit, and once the page has loaded it keeps working even with no connection.

Frequently asked questions

What is prime factorization?
It is writing a whole number as a product of prime numbers, the numbers divisible only by 1 and themselves. For 60 that is 2 × 2 × 3 × 5, usually written 2² × 3 × 5. Every whole number above one has exactly one such factorization.
How do you find the prime factors of a number?
Divide by the smallest prime that goes in evenly, then keep dividing the result the same way until you reach 1. For 60: divide by 2 to get 30, by 2 again to get 15, by 3 to get 5, and 5 is prime. The calculator does this and draws the tree.
What if the number is already prime?
Then its only prime factor is itself, and the calculator says so. A prime such as 17 cannot be broken down further, since nothing but 1 and 17 divides it.
Does this work offline and is anything sent to a server?
The calculation runs entirely in your browser, so nothing you type is sent anywhere, and once the page has loaded it keeps working with no connection. There is no sign-up and no limit on how many calculations you make.

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