Prime Factorization Calculator

Written byOleh Soloninupdated 5 October 2026

Number

Result

Factorisation2 · 2 · 2 · 3 · 3 · 5
With exponents2³ · 3² · 5
Long division
360 | 2 180 | 2 90 | 2 45 | 3 15 | 3 5 | 5 1 |
Distinct primes3
Number of divisors24
Primeno, it is composite

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.

How to use

Enter the number to factor.
Read the factorisation as a product and in exponent form, the division column and the divisor count.
A prime number factors into itself, which the calculator states plainly.

One number, one factorisation

Every whole number above one factors into primes in exactly one way, order aside — that is the fundamental theorem of arithmetic. 360 becomes 2 · 2 · 2 · 3 · 3 · 5, or 2³ · 3² · 5 in exponent form.

The exponents do more work than they look. Adding one to each and multiplying gives the divisor count: 4 × 3 × 2 = 24. Taking the shared primes at their lowest powers gives the greatest common divisor; taking every prime from either number at its highest power gives the least common multiple.

Worked out with this calculator.
Number	Factorisation	Exponent form	Divisors
97	97	97	2
360	2 · 2 · 2 · 3 · 3 · 5	2³ · 3² · 5	24
1,024	2 · 2 · … · 2	2¹⁰	11

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?

It hands you the divisor count, the greatest common divisor and the least common multiple without further work, and it is how fractions get simplified. For 360 the exponents 3, 2 and 1 give 4 × 3 × 2 = 24 divisors. 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?

It depends on the structure as much as the length: 10^200, with 201 digits, factors at once as 2^200 × 5^200. The hard cases are products of two carefully chosen large primes: in 2020 researchers factored the 250-digit RSA-250, and it took thousands of core-years. Multiplying two large primes is easy; undoing it is not, and that asymmetry is what secures RSA.

What are the prime factors of 360?

2 · 2 · 2 · 3 · 3 · 5, written 2³ · 3² · 5. Divide repeatedly by the smallest prime that fits until one remains; the calculator shows that column in full.

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

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