Common Factor Calculator

Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of numbers

Enter Numbers

About Common Factors

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6.

GCF is useful for simplifying fractions, solving ratio problems, and factoring polynomials in algebra.

The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by each of the numbers. For example, the LCM of 4 and 6 is 12.

LCM is particularly useful when adding or subtracting fractions with different denominators, solving problems involving repeating events, and in algebraic operations.

There are several methods to find GCF and LCM:

  1. Prime Factorization: Break down each number into its prime factors and multiply the common primes for GCF or all primes with highest powers for LCM.
  2. Listing Method: List all factors of each number and identify the largest common one (GCF) or list multiples to find the smallest common one (LCM).
  3. Euclidean Algorithm: An efficient method for finding the GCF of two numbers by repeatedly applying the division algorithm.

Our calculator uses the most efficient algorithms to compute both GCF and LCM instantly.

Why Use Our Common Factor Calculator?

Instant Results

Get GCF and LCM calculations in milliseconds, saving you time and effort.

Multiple Numbers

Calculate common factors for two or more numbers simultaneously.

Detailed Breakdown

See prime factorization and all common factors for better understanding.

Common Factor Calculator - Powerful Math Tool

Our Common Factor Calculator is an essential online tool for students, teachers, and professionals who work with numbers. Whether you're simplifying fractions, solving algebraic equations, or working on number theory problems, finding the greatest common factor (GCF) and least common multiple (LCM) is a fundamental mathematical operation.

Applications of GCF and LCM

Advanced Features

Unlike basic calculators, our tool provides:

Pro Tip: Bookmark this page for quick access whenever you need to find common factors or multiples. Our calculator is completely free with no registration required!