Prime Factorization Calculator
Break any whole number into its prime factors with exponents.
What the Prime Factorization Calculator does
Every whole number above 1 factors into primes in exactly one way — the fundamental theorem of arithmetic. Factorisation is how you find greatest common divisors, simplify fractions, and reduce radicals.
Formula
n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖDivisor count = (a₁+1)(a₂+1)…(aₖ+1)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Number | number | Yes | Accepts 2 or more. |
How to use it
- Enter Number.
- Select Calculate.
Worked example
Factorise 360.
- Number
- 360
360 = 2³ × 3² × 5, which gives (3+1)(2+1)(1+1) = 24 divisors.
Reading the result
- Every whole number above 1 has exactly one prime factorisation, which is what makes it a reliable fingerprint for a number.
- The GCD of two numbers is the product of the primes they share, and the LCM is the product of the highest power of every prime appearing in either.
Common mistakes
- Stopping at composite factors. 12 = 2 × 6 is a factorisation but not a prime one; 12 = 2² × 3 is.
- Including 1 as a factor. It is not prime, and including it would destroy the uniqueness of the factorisation.
Frequently asked questions
What is the fastest way to factor by hand?
Divide by 2 until it is odd, then try 3, 5, 7, 11 and so on, stopping once the trial divisor exceeds the square root of what remains.