- Greatest common factor
- 6
How it works
One common factor must fit every input
The GCF of 18 and 24 is 6, but adding 35 makes the three-number GCF equal 1. A large factor shared by one pair need not divide every value in a longer list.
Using a greatest common factor
The greatest common factor identifies the largest shared positive divisor of the entered whole numbers. It is useful for simplifying ratios and fractions or finding the largest equal grouping size. A common multiple answers a different question and can be much larger than the inputs. Review how the tool handles zeros and signs before interpreting an edge case.
Whole numbers: formula and assumptions
gcd(a,b) = gcd(b, a mod b); lcm(a,b) = |a × b| / gcd(a,b).
The Euclidean algorithm finds the greatest common divisor. Factor lists contain positive factors.
Worked example
Using the Whole numbers example:
- Whole numbers
- 12, 18, 24
gcd(a,b) = gcd(b, a mod b); lcm(a,b) = |a × b| / gcd(a,b).
Example result
Greatest common factor: 6
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
How can GCF help simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For 18/24, dividing both by 6 gives 3/4.
Is greatest common divisor different from greatest common factor?
No. GCD and GCF are two names for the same whole-number relationship.
Prepared by Finflo. See our methodology and editorial policy.