Prime Factorization Calculator

Calculate prime factorization, find all prime factors, and list all factors of a number with step-by-step solutions.

Calculator

Enter a positive integer (max: 10^15)

Enter a positive integer to find its prime factorization, prime factors, and all factors.

Complete User Guide

What is Prime Factorization?

Prime factorization is the process of expressing a number as a product of its prime factors. Every composite number can be uniquely expressed as a product of prime numbers.

Example: 12 = 2² × 3 (2 × 2 × 3)

Key Concepts

  • Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself
  • Prime Factor: A prime number that divides the given number
  • Prime Factorization: The unique representation of a number as a product of prime factors
  • Factor: A number that divides the given number without a remainder

How to Use This Calculator

  1. Enter a positive integer
  2. Click 'Calculate' to find prime factorization
  3. Review prime factors and prime factorization
  4. View all factors of the number
  5. Follow the step-by-step solution to understand the process

Examples

Example 1: Composite Number

Number: 12

Prime Factors: 2, 3

Prime Factorization: 2² × 3

All Factors: 1, 2, 3, 4, 6, 12

Example 2: Prime Number

Number: 17

Prime Factors: 17

Prime Factorization: 17

All Factors: 1, 17

Example 3: Large Number

Number: 100

Prime Factors: 2, 5

Prime Factorization: 2² × 5²

All Factors: 1, 2, 4, 5, 10, 20, 25, 50, 100

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