What is prime factorization?

Prime factorization expresses a number as a product of prime numbers. For example, 360 = 2^3 × 3^2 × 5, meaning 2 × 2 × 2 × 3 × 3 × 5.

What happens if I enter a prime number?

The tool tells you the number is prime, since a prime number has no factors other than 1 and itself.

How does the tool find the factors?

It divides out the smallest factor repeatedly, starting at 2, counting how many times each prime divides the number. When the remaining part is 1, every prime factor and its power has been found.

Why is prime factorization unique?

The fundamental theorem of arithmetic guarantees every whole number greater than 1 has exactly one prime factorization (apart from the order of factors). So there is a single correct answer for any input.

What is prime factorization used for?

It is the basis for finding the greatest common divisor and least common multiple, simplifying fractions, and underlies cryptography, where the difficulty of factorizing very large numbers keeps data secure.

What does the exponent form mean?

Exponent form groups repeated primes: 2^3 means 2 appears three times (2 × 2 × 2). It is a compact way to write the factorization, e.g. 360 = 2^3 × 3^2 × 5.

Is any data uploaded?

No — the factorization is computed entirely in your browser. Nothing is sent anywhere.

Prime Factorization Calculator

Prime factorization calculator

Enter any whole number and instantly see its prime factorization — the unique product of prime numbers that make it up, shown in exponent form like 360 = 2^3 × 3^2 × 5. It is useful for simplifying fractions, finding GCDs and LCMs, and understanding the building blocks of a number.

How it works

The tool uses trial division, dividing out each prime factor completely before moving on:

start at d = 2
while d × d ≤ remaining:
  while remaining is divisible by d: divide it out, count the power
  move to the next d
if remaining > 1, it is itself a prime factor

Counting how many times each prime divides gives the exponent form. If nothing smaller than the number divides it, the number is reported as prime.

Example

Factorizing 360:

360 ÷ 2 = 180 ÷ 2 = 90 ÷ 2 = 45 → 2 appears 3 times
45 ÷ 3 = 15 ÷ 3 = 5 → 3 appears 2 times
5 is prime → 5 appears 1 time
Result: 360 = 2³ × 3² × 5

Number	Prime factorization
12	2² × 3
100	2² × 5²
360	2³ × 3² × 5
97	97 (prime)

Everything runs locally in your browser, so your numbers never leave your device.