01
How to use this calculator
- Enter two or more whole numbers.
- Compare their factors or apply the Euclidean algorithm.
- Use the GCF to simplify fractions or divide quantities into equal groups.
02
A little understanding goes a long way.
The greatest common factor, also called GCD or HCF, is the largest positive integer shared by the factor lists. The Euclidean algorithm repeatedly replaces a pair with the smaller number and the remainder.
THE FORMULA
gcd(a, b) = gcd(b, a mod b)
TRY IT ON PAPER
A worked example
The common factors of 18 and 24 are 1, 2, 3 and 6. Their greatest common factor is 6.
03
A few common questions
Is GCF the same as GCD?
Yes. Greatest common factor, greatest common divisor and highest common factor describe the same quantity.
What about zero?
The GCF of a nonzero integer and zero is the absolute value of the nonzero integer. The all-zero case requires an explicit convention.