Prime Factorization Calculator

Prime Factorization Calculator breaks a number into the primes that multiply to make it, with exponents, and shows the division steps that got there. Three hundred and sixty is 2^3 x 3^2 x 5, and every number above one has exactly one such factorisation -- a fact so central it is called the fundamental theorem of arithmetic.

The divisor count comes straight out of the factorisation rather than being found by trial. Add one to each exponent and multiply: for 360 that is four times three times two, which is twenty-four divisors. That shortcut is worth knowing, and the working shows it applied to your number.

The full divisor list is optional because it grows quickly and is rarely the thing you came for. When it is, it is sorted and complete, found by pairing each divisor below the square root with its partner above -- the same trick that makes primality testing fast.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

• Shows prime factorisation, distinct primes, prime factors with repeats, number of divisors and sum of divisors together, so you are not running it twice
• A results table you can read across
• Prints the formula with your own figures substituted in
• Updates as you type, with no button to press and no page reload
• Copy the result in one click
• Free, no sign-up, and it runs entirely in your browser

The prime factorization calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Simplifying fractions or surds
• Finding every divisor of a number
• Working out the GCF or LCM by hand
• Checking a factor tree in homework