What the greatest common factor is
It is the largest number that divides evenly into each number in the list.
The factors of 12 are 1, 2, 3, 4, 6 and 12, and the factors of 18 are 1, 2, 3, 6, 9 and 18, so the greatest common factor is 6.
Worked example
For 12 and 18 the greatest common factor is 6. The least common multiple of the same pair is 36.
For 24 and 36 the greatest common factor is 12, because both divide by 12 and no larger number works.
Where it is used
Reducing a fraction to lowest terms means dividing the numerator and denominator by their greatest common factor. 12/18 becomes 2/3.
Splitting items into equal groups with nothing left over uses the same idea.
Inputs for the greatest common factor calculator
Whole numbers
Two or more whole numbers, separated by commas or spaces. Negative signs are ignored and zero is not allowed.
CALCULATOR QUESTIONS
Greatest common factor calculator questions
What is the greatest common factor of 12 and 18?
6, because 6 divides into both and no larger number does.
Is the greatest common factor the same as the highest common factor?
Yes. US courses say greatest common factor and UK schools say highest common factor.
What is the GCF of 24 and 36?
12. Both divide by 12, and 24 does not divide 36.
What if the numbers share no factor?
The answer is 1. Numbers such as 8 and 9 share only the factor 1.