Prime Factorization Calculator

Prime Factorization

Prime Factors

Factor Tree

All Divisors

About Prime Factorization Calculator

What Is Prime Factorization?

Prime factorization is the process of breaking down a composite number into a product of prime numbers. Every positive integer greater than 1 can be expressed uniquely as a product of primes (this is the Fundamental Theorem of Arithmetic). For example, 360 = 2^3 x 3^2 x 5. No matter how you factor 360, you always end up with the same primes. Prime factorization is used in cryptography (RSA encryption relies on difficulty of factoring large numbers), simplifying fractions, finding GCF and LCM, and solving number theory problems.

How to Find Prime Factors

Start by dividing the number by the smallest prime (2). If divisible, record 2 as a factor and divide. Continue dividing by 2 until it no longer divides evenly. Move to the next prime (3), then 5, 7, 11, and so on. Continue until the quotient is 1. The collection of all primes used in the division is the complete factorization. You only need to check primes up to sqrt(n) because if n has a factor larger than its square root, the complementary factor must be smaller.

How to Use This Calculator

Enter any positive integer and click Factorize. The calculator shows the complete prime factorization in exponential form, lists all prime factors, displays the total number of divisors, shows all divisors of the number, and indicates whether the number itself is prime.

Frequently Asked Questions

Is 1 a prime number?

No. By mathematical convention, 1 is neither prime nor composite. Primes must have exactly two distinct positive divisors: 1 and themselves. The number 1 has only one divisor.

How many divisors does a number have?

If n = p1^a x p2^b x p3^c, the total number of divisors is (a+1)(b+1)(c+1). For 360 = 2^3 x 3^2 x 5^1: (3+1)(2+1)(1+1) = 24 divisors.

Why is prime factorization important for encryption?

RSA encryption multiplies two very large primes. The resulting product is public, but factoring it back into the original primes is computationally infeasible, securing the encryption.