Prime Factorization Calculator - Factor Numbers into Primes

Prime factorization expresses a number as a product of prime numbers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). Prime numbers are divisible only by 1 and themselves.

1. 1

   Enter Number

   Input the positive integer you want to factorize

2. 2

   Start Division

   The calculator begins dividing by the smallest prime (2)

3. 3

   Continue Process

   Division continues with increasing primes until the quotient is 1

4. 4

   View Results

   The complete prime factorization is displayed

• 1

  Prime numbers are only divisible by 1 and themselves

• 2

  2 is the only even prime number

• 3

  To test primality, check divisibility by primes up to sqrt(n)

• 4

  For GCD from prime factors, use the smallest power of each common prime

• Considering 1 as a prime number - primes start from 2

• Forgetting to include repeated prime factors - 8 = 2^3, not just 2

• Stopping before complete factorization - continue until quotient is 1

• Not checking all necessary primes - test up to the square root of the number