What is the GCD Calculator?
Find the greatest common divisor (GCD) or highest common factor (HCF) of two or more positive integers with this free online GCD calculator. Enter numbers separated by commas and get the GCD, LCM, prime factorizations, Euclidean algorithm steps, and a full worked solution. Runs entirely in your browser with no signup.
How to use the GCD Calculator
- Enter at least two positive integers (comma, space, or newline separated).
- Click Calculate GCD.
- Review the GCD and LCM results.
- Follow the Euclidean algorithm division steps.
- Copy the GCD or the full summary with steps.
Common use cases
- Finding GCD(48, 18) = 6 to simplify the fraction 48/18
- Computing GCD(24, 36, 60) = 12 for a number theory problem
- Checking that GCD(5, 7) = 1 means the numbers are coprime
Frequently asked questions
- What is the greatest common divisor (GCD)?
- The GCD of a set of numbers is the largest positive integer that divides every number in the set without a remainder. For example, GCD(48, 18) = 6.
- What is the Euclidean algorithm?
- It repeatedly divides the larger number by the smaller and replaces the larger with the remainder until the remainder is 0. The last non-zero remainder is the GCD.
- Is GCD the same as HCF?
- Yes. GCD (greatest common divisor) and HCF (highest common factor) are the same quantity.
- How many numbers can I enter?
- Between 2 and 20 positive integers, each up to 10 billion.
