Factor Calculator

Prime Factorization

Break down any integer greater than 1 into its unique product of prime numbers.

What is Prime Factorization?

Prime factorization is the process of breaking down a composite number into a product of prime numbers that multiply to the original number. According to the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorization. For example, 60 factors uniquely into 2 × 2 × 3 × 5, or 2² × 3 × 5.

Finding the prime factors is a crucial algebraic step used to find Greatest Common Factors (GCF), Least Common Multiples (LCM), and to simplify square roots or fractions.

Interactive Factor Tree

Select a number to build its unique factor tree. Blue circles are prime leaf factors.

Factor Tree Diagram

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Prime FactorComposite Factor

Examples of Prime Factorization

See factor trees and final prime products for standard numbers.

362² × 3²

36 is a perfect square (6²). Its tree splits into 2 × 18, then 18 into 2 × 9, and 9 into 3 × 3. The prime leaf nodes are 2, 2, 3, 3, giving 2² × 3².

602² × 3 × 5
842² × 3 × 7

Frequently Asked Questions

By definition, a prime number must be greater than 1. Including 1 would violate the uniqueness of prime factorization (e.g. 6 = 2×3 = 2×3×1 = 2×3×1×1...).