Prime Factorization Calculator

Every whole number greater than 1 is a unique product of primes. This calculator finds it and shows each division.

Factorize a number

Prime factorization of 3602³ × 3² × 5
Expanded form
2 × 2 × 2 × 3 × 3 × 5
Distinct prime factors
2, 3, 5
Number of divisors
24

Working

  1. 360 ÷ 2 = 180
  2. 180 ÷ 2 = 90
  3. 90 ÷ 2 = 45
  4. 45 ÷ 3 = 15
  5. 15 ÷ 3 = 5
  6. 5 ÷ 5 = 1

The method

Divide by the smallest prime that goes in exactly, write it down, and repeat with the quotient until you reach 1. The primes you divided by are the prime factors. By the fundamental theorem of arithmetic, the result is the same whatever order you find them in.

Worked example

Prime factorization of 360

  1. 360 ÷ 2 = 180
  2. 180 ÷ 2 = 90
  3. 90 ÷ 2 = 45
  4. 45 ÷ 3 = 15
  5. 15 ÷ 3 = 5
  6. 5 ÷ 5 = 1

360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5

What the factorization tells you

  • Number of divisors: add 1 to each exponent and multiply — (3 + 1)(2 + 1)(1 + 1) = 24 divisors for 360.
  • Perfect squares have only even exponents; perfect cubes have exponents divisible by 3.
  • GCF and LCM of several numbers come straight from their factorizations.
  • Simplifying radicals: √360 = √(2² × 3² × 10) = 6√10.