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Math

Prime Factorization Calculator

Break a positive whole number into its prime factors and show repeated factors as powers.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter whole number.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Repeatedly divide by each candidate factor beginning at 2. After removing a factor completely, continue until the candidate squared exceeds the remaining value. Any remainder above 1 is prime.

A WORKED EXAMPLE

360 = 2³ × 3² × 5. Multiplying those factors gives 360.

What to keep in mind

Accepts whole numbers from 2 through one trillion. Zero, one, negative numbers and fractions are outside the supported domain.

Common questions

What happens when the number is prime?

The output is the original number because it has no smaller prime factors.

Is 1 a prime number?

No. Prime numbers have exactly two positive divisors; 1 has only one.

Methodology maintained by ClarityKit. How these tools are built and checked.