Prime Factorization Calculator

Number

Result

Factorisation2 × 2 × 2 × 3 × 3 × 5
With exponents2^3 × 3^2 × 5
Distinct primes3
Number of divisors24
Primeнет, число составное

The fundamental theorem of arithmetic at work

Canonical factorisation with exponents, the count of distinct primes, and the number of divisors that follows directly from it.

Every whole number above one factors into primes in exactly one way — that is the fundamental theorem of arithmetic. The order can vary, the multiset of factors cannot.

Factorisation is a working tool rather than a curiosity. From it you get the greatest common divisor and least common multiple of two numbers, the divisor count, and whether a fraction with that denominator will repeat.

What this calculator shows

The factorisation written out and in canonical exponent form
How many distinct primes are involved
The divisor count, derived straight from the exponents

What to keep in mind

Factorisation is defined from two upwards; one has no prime factors and zero cannot be factorised at all.
Trial division runs to the square root, so numbers up to a trillion resolve quickly.

FAQs

What is factorisation good for?

Simplifying fractions, finding GCD and LCM, counting divisors, and understanding a number's structure. In cryptography the difficulty of factorising huge numbers is what RSA rests on.

How do I get the GCD from factorisations?

Take the shared primes at their lowest exponents. For 360 = 2³ × 3² × 5 and 84 = 2² × 3 × 7, the shared part is 2² × 3 = 12.

Why isn't one a prime?

Because factorisation would stop being unique — you could append any number of ones. The definition excludes it deliberately.

How hard is factorising a very large number?

Practically impossible at a few hundred digits with current hardware. Multiplying two large primes is easy; undoing it is not, and that asymmetry is what secures RSA.

Worked example

Factorise 360

Input: 360

Output: 2³ × 3² × 5, with 24 divisors

Note: The divisor count comes from the exponents plus one: (3+1) × (2+1) × (1+1) = 24. No need to list the divisors themselves.

Useful links

All tools in Math & Statistics

Prime Factorization Calculator

Result

Related tools

Divisors Calculator

Prime Number Checker

GCD & LCM Calculator

Useful links