Math & School

Prime factorization calculator

Decompose a number into prime factors, with a worked example and prime check.

Updated on May 25, 2026 Calculator, calculation path and examples on one page

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Calculator

Examples

360 = 2³ · 3² · 5.

Prime factorization: 360 = 2³ · 3² · 5

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84 = 2² · 3 · 7.

Prime factorization: 84 = 2² · 3 · 7

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97 is a prime number.

Prime factorization: 97 = 97

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FAQ

What is prime factorization?

Every natural number starting from 2 can be written uniquely as a product of prime numbers, for example 360 = 2³ · 3² · 5.

What is a prime number?

A prime number is a natural number greater than 1 that is only divisible by 1 and itself, such as 2, 3, 5, 7, 11.

How do I tell if a number is prime?

If the prime factorization consists only of the number itself, it is a prime number.

Why do you need prime factorization?

Among other things, for determining gcd and kgv as well as for abbreviating fractions.

Up to what number does the calculator work?

Up to 1,000,000,000. Very large numbers are deliberately excluded so that the calculation remains quick.

What does the exponent of 2³ mean?

It indicates how often the prime factor occurs. 2³ means 2 · 2 · 2.

Related calculators

Calculate the greatest common divisor (GCD) and least common multiple (LCM).

Reduce, expand, add, subtract, multiply and divide fractions.

Convert numbers between binary, decimal, octal and hexadecimal.

Sources and notes

methodology: Trial division by increasing divisors up to the root of the number.