# Prime Factorization Calculator

Break an integer into prime factors, show the factorization string, and optionally include divisor properties and factorization steps

> Canonical page: https://elysiatools.com/en/tools/prime-factorization-calculator

- **Category:** Math & Numbers

- **Keywords:** prime factorization, prime factors, number theory, calculator, math

## Overview

The Prime Factorization Calculator is a mathematical utility designed to break down any integer into its fundamental prime factors. It instantly generates the factorization string in exponential notation and can optionally display step-by-step division processes and detailed divisor properties, making it an essential tool for students, educators, and programmers working with number theory.

## Inputs

- **Number Input** (text): Enter an integer such as 360
- **Show Factorization Steps** (checkbox)
- **Include Divisor Properties** (checkbox)

## When to use

- When simplifying fractions or finding the greatest common divisor (GCD) and least common multiple (LCM) of multiple numbers.
- When studying number theory concepts or verifying manual prime factorization homework.
- When analyzing the divisor properties of large integers for algorithmic programming or cryptography.

## How it works

- Enter the integer you want to factorize into the primary number input field.
- Toggle the checkboxes to include step-by-step factorization details or calculate divisor properties based on your needs.
- Submit the request to instantly receive a structured JSON output containing the prime factors, exponents, and the complete factorization string.

## Use cases

- Mathematics students checking their manual prime tree calculations for homework assignments.
- Programmers generating test cases for algorithms involving prime numbers, GCD, or LCM.
- Educators creating step-by-step factorization examples for classroom demonstrations.

## Frequently asked questions

### What is prime factorization?

Prime factorization is the process of breaking down a composite number into a set of prime numbers that multiply together to result in the original number.

### Can this tool handle negative numbers or decimals?

No, prime factorization is only defined for positive integers greater than 1. Please enter a valid positive whole number.

### What are divisor properties?

Divisor properties include the total count of divisors and the sum of all divisors for the given number, which the tool can calculate automatically.

### How does the tool display the result?

The result is returned as structured JSON, including an easy-to-read factorization string (e.g., 360 = 2^3 × 3^2 × 5) and an array of individual prime bases and their exponents.

### Are the factorization steps shown?

Yes, if you enable the 'Show Factorization Steps' option, the output will include the sequential division steps used to reach the final prime factors.

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