Greatest Common Factor Calculator
Find the greatest common factor (GCF) or greatest common divisor (GCD) of two or more numbers. Enter up to 10 numbers and get the GCF with step-by-step calculations and prime factorization.
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Quick Examples:
Methods to Find GCF
1. Prime Factorization Method
Find the prime factorization of each number, then take the lowest power of each common prime factor.
2. Euclidean Algorithm
Repeatedly apply the division algorithm until the remainder is zero. Works best for two numbers.
3. Listing Factors Method
List all factors of each number and find the largest common factor.
How to Use This Calculator
Applications of GCF
Real-World Applications
- Simplifying fractions to lowest terms
- Dividing objects into equal groups
- Finding common tile sizes for flooring
- Determining gear ratios in machinery
- Organizing items in equal rows and columns
- Scaling recipes proportionally
Mathematical Applications
- Reducing fractions to simplest form
- Solving linear Diophantine equations
- Finding rational approximations
- Modular arithmetic calculations
- Cryptography and number theory
- Algorithm optimization
Example Calculations
Example 1: Two Numbers
Find GCF(72, 48):
Example 2: Three Numbers
Find GCF(60, 90, 120):
Example 3: Coprime Numbers
Find GCF(15, 28):
Frequently Asked Questions
What's the difference between GCF and LCM?
GCF (Greatest Common Factor) is the largest number that divides all given numbers, while LCM (Least Common Multiple) is the smallest positive number that is divisible by all given numbers.
What does it mean when GCF is 1?
When the GCF is 1, the numbers are called coprime or relatively prime. This means they share no common factors other than 1, such as 15 and 28.
Can GCF be larger than the smallest input number?
No, the GCF is always less than or equal to the smallest input number. It equals the smallest number only when that number divides all other input numbers.