Greatest Common Factor (GCF) Calculator
Calculate the greatest common divisor of multiple numbers instantly with our free online tool
Calculate GCF
Result:
How It Works
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.
Calculation Method:
This calculator uses the Euclidean algorithm to compute the GCF efficiently:
- Start with two numbers
- Divide the larger number by the smaller number
- Replace the larger number with the smaller number and the smaller number with the remainder
- Repeat until the remainder is zero
- The divisor at this point is the GCF
Example:
For numbers 24 and 36:
36 ÷ 24 = 1 remainder 12
24 ÷ 12 = 2 remainder 0
Thus, GCF(24, 36) = 12
This calculator saved me so much time on my math homework. Accurate and easy to use!
As a math teacher, I appreciate how this tool shows the step-by-step process. Great learning aid!
Perfect for quick calculations. Wish it could handle more than 10 numbers at once though.
Understanding the Greatest Common Factor
What is the GCF?
The Greatest Common Factor (GCF) of two or more integers is the largest positive integer that divides each of the numbers without leaving a remainder. For example, the GCF of 8 and 12 is 4.
Applications of GCF
GCF has numerous practical applications:
- Simplifying fractions: Reduce fractions to their simplest form
- Algebra: Factor polynomials and simplify algebraic expressions
- Number theory: Solve Diophantine equations and understand number properties
- Real-world problems: Divide items into equal groups, pattern recognition, and cryptography
Different Methods to Find GCF
Besides the Euclidean algorithm used in this calculator, there are other methods:
- Prime Factorization: Factor each number into primes and multiply common factors
- Listing Factors: List all factors of each number and find the greatest common one
- Binary Method: Efficient algorithm especially for large numbers