GCF Calculator
Find the greatest common factor (GCF) of 2 to 4 numbers using the Euclidean algorithm.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter 2 to 4 numbers and the calculator instantly finds their greatest common factor. The step-by-step breakdown shows each GCF calculation using the Euclidean algorithm.
- Enter at least two numbers. Type the numbers you want to find the GCF of.
- Add more numbers (optional). The third and fourth fields handle cases where you need the GCF of three or four numbers.
- Read the result. The GCF appears with the calculation steps showing how it was derived.
The GCF (also called GCD or HCF) is the largest number that divides evenly into all given numbers. It is calculated using the Euclidean algorithm, which is efficient even for very large numbers.
About the Greatest Common Factor
The greatest common factor is the largest positive integer that divides each of the given numbers without a remainder. It is used in simplifying fractions (divide numerator and denominator by their GCF), solving problems involving repeated patterns, and in number theory.
The Euclidean algorithm finds the GCF by repeatedly dividing the larger number by the smaller and taking the remainder, until the remainder is zero. The last non-zero remainder is the GCF. For multiple numbers, the GCF is found iteratively: GCF(a, b, c) = GCF(GCF(a, b), c).
Frequently Asked Questions
What is the difference between GCF, GCD, and HCF?
They are different names for the same thing. GCF (Greatest Common Factor) and HCF (Highest Common Factor) are used in the US and UK respectively. GCD (Greatest Common Divisor) is the standard mathematical term. All refer to the largest number that divides evenly into two or more numbers.
How do you find the GCF of two numbers?
Use the Euclidean algorithm: divide the larger number by the smaller, take the remainder, then divide the smaller number by the remainder. Repeat until the remainder is zero. The last non-zero remainder is the GCF. For example, GCF(24, 36): 36 / 24 = 1 remainder 12, then 24 / 12 = 2 remainder 0. The GCF is 12.
What is the relationship between GCF and LCM?
For two numbers a and b: GCF(a, b) x LCM(a, b) = a x b. This means if you know the GCF, you can find the LCM by dividing the product of the two numbers by the GCF.