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Prime Factorization Calculator

Prime factors, exponent form and a factor tree.

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Factor tree

Every divisor

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Powers of each prime

PrimeExponentContributes

Prime factorisation

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Properties

Is it prime?—
Distinct primes—
Number of divisors—
Sum of divisors—

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From the sum of its proper divisors

Every integer above 1 has exactly one prime factorisation, ignoring order — the fundamental theorem of arithmetic. The number of divisors follows from it: add one to each exponent and multiply. Only primes up to the square root need testing, because any larger factor already has a smaller partner.

Quick Tool Overview

The Prime Factorization Calculator breaks a number into the primes that multiply to make it, shown as a product and in exponent form, with a factor tree drawn out and the complete list of divisors generated from the factorisation.

What it does
Decomposes a number into its prime factors
You give it
Any whole number from 2 upwards
You get back
Prime factors, a factor tree and every divisor
Best for
Homework, fraction simplification and number theory
Calculators Free, unlimited use No sign-up Runs in your browser

About the Prime Factorization Calculator

Decompose a number into the primes that multiply to make it, shown both as a plain product and in exponent form. A factor tree is drawn out, and the complete list of divisors is generated from the factorisation.

Every integer greater than one has exactly one prime factorisation, ignoring the order of the factors — this is the fundamental theorem of arithmetic, and it is why primes are described as the building blocks of the integers. The factorisation also answers questions that look unrelated: the number of divisors is found by adding one to each exponent and multiplying, and greatest common divisors and least common multiples both fall straight out of comparing two factorisations.

Key features of the Prime Factorization Calculator

Factor tree drawn out

Each division step is shown, which is usually exactly what a homework question asks you to produce.

Exponent form

360 shown as 2³ × 3² × 5 rather than a long repeated product.

Every divisor generated

The full divisor list, its count and its sum, all derived from the factorisation rather than by brute force.

Primality reported

If the number is itself prime, the tool says so instead of returning a one-item list without comment.

Efficient trial division

Only primes up to the square root are tested, so large numbers factor quickly.

How to use the Prime Factorization Calculator

  1. 1

    Enter a whole number

    Anything from 2 upwards. Large values are handled with trial division up to the square root.

  2. 2

    Read the factorisation

    As a product of primes and in exponent form.

  3. 3

    Follow the factor tree

    Each division step is shown, which is usually what homework asks you to draw.

  4. 4

    Use the divisor list

    Every divisor is generated, along with how many there are and their sum.

Frequently asked questions

Writing a number as a product of prime numbers. 360 factorises to 2³ × 3² × 5, and by the fundamental theorem of arithmetic that decomposition is unique.

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