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Prime Factorization Calculator

Prime factorization expresses a natural number as a product of prime numbers. Every natural number greater than 1 has a unique prime factorization, which is also the basis for finding the GCD and LCM.

Enter a natural number to find its prime factors and exponents using trial division.

For example, the prime factorization of 60 is 2² × 3 × 5.

Prime Factorization Calculator Calculation Method

Divide by the smallest prime numbers in order, repeating until it can no longer be divided.

About This Calculator

Prime factorization breaks a whole number into the primes that multiply together to make it. Every integer greater than 1 has exactly one such factorization, which is why primes are called the building blocks of the number system.

Enter a natural number to get its prime factors and their exponents, written in exponential form.

The prime factorisation of an integer is unique apart from order, which is the fundamental theorem of arithmetic. Test divisors only up to the square root: for 1,443 that means primes up to 37, and the answer is 3 × 13 × 37. That cost, trivial for small numbers, is what makes public-key cryptography based on large primes possible.

Key Formula:N = p₁^a × p₂^b × … (p prime, a,b ≥ 1)

Frequently Asked Questions

What is a prime number?

A prime is a whole number greater than 1 whose only divisors are 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13; note that 1 is not prime and 2 is the only even prime.

Why is prime factorization important?

It underpins cryptography: RSA encryption relies on the fact that multiplying two large primes is easy, but factoring the product back into those primes is extremely hard for computers.

How do I factor a quadratic quickly?

Look for two numbers whose product is the constant term and whose sum is the middle coefficient. For x² − 5x + 6 the pair −2 and −3 works, giving (x − 2)(x − 3).

Why can testing stop at the square root?

If n = a × b with both factors greater than √n, then a × b > n, which is impossible. At least one factor must sit at or below the square root, so no divisor above it can be the first one found.

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Sources & last update

2026-10-19