GCD Calculator

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Find the Greatest Common Divisor (GCD), also known as HCF or GCF, of two or more numbers.

Input Numbers

First Number

Second Number

Calculation Results

Greatest Common Divisor (GCD)

The largest positive integer that divides each of the integers.

Least Common Multiple (LCM)144

Simplified Ratio8 : 3

About this calculator

What is GCD?

The Greatest Common Divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. It is also known as the Greatest Common Factor (GCF), Highest Common Factor (HCF), or Greatest Common Measure (GCM). For example, the GCD of 8 and 12 is 4.

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Pro Tips

The GCD is used to simplify fractions to their lowest terms.
If the GCD of two numbers is 1, they are called 'relatively prime' or 'coprime'.
The relationship between GCD and LCM is: GCD(a, b) × LCM(a, b) = |a × b|.

Fun Facts

"The Euclidean Algorithm, used to find the GCD, is one of the oldest algorithms still in common use, dating back to 300 BC."
"The GCD of two numbers is related to tiles: if you have a floor of a × b, the GCD is the size of the largest square tile that can tile the floor without gaps."
"Cryptography systems like RSA rely heavily on the properties of GCD and prime numbers."

Formula: GCD(a, b) = GCD(b, a mod b)