GCD Calculator
Find the Greatest Common Divisor (GCD), Greatest Common Factor (GCF), or Highest Common Factor (HCF) of two or more integers.
Find the Greatest Common Divisor (GCD), Greatest Common Factor (GCF), or Highest Common Factor (HCF) for any set of 2 or more integers.
Formula & Method
- Euclidean Algorithm:
GCD(a, b) = GCD(b, a mod b)until remainder is0. - For 3+ Numbers:
GCD(a, b, c) = GCD(GCD(a, b), c)
Worked Example
For numbers 24, 36, 60:
GCD(24, 36) = 12GCD(12, 60) = 12
Frequently Asked Questions
What is the difference between GCD, GCF, and HCF?+
There is no mathematical difference. Greatest Common Divisor (GCD), Greatest Common Factor (GCF), and Highest Common Factor (HCF) are three terms for the exact same number—the largest positive integer that divides all given numbers without a remainder.
Which algorithm does this tool use?+
It uses the Euclidean algorithm, an efficient ancient mathematical technique based on the principle that the GCD of two numbers also divides their difference.
Can I calculate the GCD / GCF of more than two numbers?+
Yes. Separate 3 or more integers using commas or spaces to find their common GCD.