Prime Factorization Calculator

Find prime factors, exponent form, factor trees, and divisibility details with this free prime factorization calculator.

Calculate Prime Factorization

360 = 2 × 2 × 2 × 3 × 3 × 5
360 ÷ 9 = 40
Your result will appear here.

How prime factorization works

Step 1:
Divide the number by the smallest prime possible.

Step 2:
Keep dividing until the remaining value is prime.

Step 3:
List all prime factors and group repeats with exponents.

Factor tree:
Break the number into factor pairs until every branch ends in a prime.

Why prime factorization matters

Prime factorization is useful for simplifying fractions, finding greatest common factors, least common multiples, and solving many number theory problems.

It is also helpful in algebra, divisibility checks, and understanding how numbers are built.

What your result means

Your result shows the prime factors of the number, how often each factor appears, and a factor tree view when factorization mode is used.

In divisibility mode, the result shows whether one whole number divides evenly into another.

Prime factorization calculator tips

Frequently asked questions

What is prime factorization?

Prime factorization is writing a number as a product of prime numbers.

What is a prime number?

A prime number has exactly two positive factors: 1 and itself.

Why is prime factorization unique?

Every whole number greater than 1 has only one prime factorization, apart from the order of the factors.

Can 1 be prime?

No. The number 1 is not prime because it has only one positive factor.