Prime Factorization Calculator

How to Factor a Number into Primes

Prime factorization breaks a number down into prime numbers (numbers only divisible by 1 and themselves) that multiply together to give the original number.

Step-by-step method

  1. Start with the smallest prime, 2. Divide the number by 2 as many times as possible.
  2. Move to the next prime (3, 5, 7, 11, ...) and divide as many times as possible.
  3. Repeat until what remains is 1 or a prime number itself.
  4. Write all the primes you divided by as a multiplication chain.

Worked example

Factor 84: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7, and 7 is prime. So 84 = 2 × 2 × 3 × 7 or 2² × 3 × 7.

Why it matters

Prime factorization is the foundation for finding GCF and LCM, simplifying fractions, and understanding number theory. Every integer greater than 1 has exactly one unique set of prime factors.