Prime Factorization

Enter any positive integer and instantly see its prime factorization in exponential notation, a visual factor tree drawn on canvas, and a step-by-step division walkthrough.

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Integers from 2 to 10,000,000

Factor tree · Exponential form · Steps

What Is Prime Factorization?

n = p₁^a × p₂^b × p₃^c × ···

A prime number is any integer greater than 1 that has no positive divisors other than 1 and itself — such as 2, 3, 5, 7, 11, 13 …

A composite number is any integer greater than 1 that is not prime — it can be divided evenly by at least one number other than 1 and itself.

Prime factorization breaks a composite number down into a product of primes. The Fundamental Theorem of Arithmetic guarantees this decomposition is unique (up to ordering of the factors).

Every composite number can be decomposed into prime factors in exactly one way — the same primes, the same exponents, every time.

Why Does It Matter?

Prime factorization is foundational across all of mathematics. Key applications include:

Finding the Greatest Common Factor (GCF) of two numbers
Finding the Least Common Multiple (LCM) of two numbers
Simplifying fractions by canceling common factors
Simplifying square roots and radicals (e.g., √360 = 6√10)
Adding and subtracting fractions with unlike denominators
Understanding divisibility rules and number properties
Foundational to RSA encryption and modern cryptography

Prime Factorization

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