LOOZORA

Free Prime Factorization Calculator & Solver

Welcome to the Prime Factorization Calculator. This free tool breaks down any integer into its building blocks—its prime factors. It also automatically formats the result into exponential notation (e.g., writing 2 × 2 × 2 as 23) for your math homework.

Use the Prime Factorizer

Enter any positive number greater than 1 to see its factors instantly.

Prime Factorization Tool

How to Use This Tool

  1. Enter an integer (e.g., 100, 72, 360).
  2. Click “Find Prime Factors”.
  3. The result will show the full multiplication string.
  4. If applicable, it will also show the Exponential Notation below the result.

What is Prime Factorization?

Every composite number (a number that is not prime) is made by multiplying prime numbers together. These prime numbers are called “factors.”

Prime Factorization is the process of finding exactly which prime numbers need to be multiplied to get the original number.

Example: The Number 12

  • 12 can be divided by 2 → 6
  • 6 can be divided by 2 → 3
  • 3 is a prime number.
  • Result: 2 × 2 × 3 = 12.

Why is this Useful?

Prime factorization is the “DNA” of a number. It is essential for:

  • Finding the Greatest Common Divisor (GCD).
  • Finding the Least Common Multiple (LCM).
  • Cryptography (how computers secure data/passwords).
  • Simplifying square roots and fractions.

How to Do It Manually (Factor Tree Method)

If you don’t have our calculator handy, the easiest way is to build a “Factor Tree.”

  1. Write your number at the top.
  2. Find any pair of numbers that multiply to make it.
  3. Branch out. If a number is prime, circle it and stop that branch.
  4. If a number is not prime, break it down further.
  5. Continue until all branch ends are prime numbers.

Example: Factor Tree for 72

  • 72 breaks into 8 × 9
  • 8 breaks into 4 × 2 (2 is prime)
  • 4 breaks into 2 × 2 (Both prime)
  • 9 breaks into 3 × 3 (Both prime)
  • Collect all the primes: 2, 2, 2, 3, 3
  • Final Answer: 23 × 32

Frequently Asked Questions

Q: Is 1 a prime factor?
A: No. By definition, prime numbers must be greater than 1. Therefore, 1 is never listed in prime factorization.

Q: What is the prime factorization of a prime number?
A: It is simply the number itself. For example, the prime factorization of 13 is just 13.