Greatest Common Factor CalculatorFree online math calculator — instant results, no sign-up

GCF(n₁, n₂, n₃, ...) = gcd(gcd(n₁, n₂), n₃, ...)
Where gcd(a, b) = gcd(b, a mod b) until b = 0, with gcd(a, 0) = |a|

• n₁, n₂, ...Individual integer values supplied in the input list
• gcd(a, b)The greatest common divisor of two integers, calculated via the Euclidean algorithm
• a mod bThe integer remainder after dividing a by b

The tool parses the input text into an array of integers and applies an iterative reduce function. It computes the greatest common divisor of the first two numbers using the Euclidean algorithm, then computes the GCD of that result with the next number, continuing through the entire list to find the overall GCF.

These are the calculator's starting values and the results it actually produces for them.

1. 1Parse the input string into a list of individual integer values.
2. 2Calculate the greatest common divisor of the first two numbers using Euclidean division (repeated remainder reduction).
3. 3Take the resulting divisor and calculate its greatest common divisor with the next integer in the list.
4. 4Repeat this reduction until all integers have been processed, returning the final common divisor as the GCF.

Further reading

• Wolfram MathWorld: Greatest Common Divisor
• Khan Academy: Greatest Common Factor