What is prime factorization?

Prime factorization is the process of expressing a positive integer as a product of prime numbers. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).

What is the largest number this calculator can handle?

The calculator handles integers up to 15 digits. Very large numbers with large prime factors may take a moment to compute, but results are shown instantly for most practical inputs.

No. By mathematical convention, 1 is neither prime nor composite. This calculator requires inputs of 2 or greater to produce a prime factorization.

What does exponential notation mean in the results?

Exponential notation groups repeated prime factors using exponents. For example, 12 = 2 x 2 x 3 is written as 2^2 x 3^1 in exponential form, which is more compact and easier to read.

How is this useful for finding GCD and LCM?

Once you know the prime factorizations of two numbers, the GCD is the product of the lowest powers of common primes, and the LCM is the product of the highest powers of all primes that appear.

Can I factorize a prime number?

Yes. A prime number's factorization is just itself. For example, the prime factorization of 13 is simply 13^1.

Prime Factorization Calculator

Name: Prime Factorization Calculator
Availability: InStock
Author: Nham Vu

Enter any positive integer to instantly find its prime factorization with all prime factors and their exponents.

Enter a Number

Positive integer

Enter any integer from 2 to 999,999,999,999,999

Try an example

Enter a number and press Factorize to see the prime factors.

Product Notation

Exponential Notation

Distinct Prime Factors

Step-by-Step Division

Step	Dividend	Divisor (Prime)	Quotient

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