GCD Calculator
Find the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of two or more integers.
Greatest Common Divisor (GCD / HCF)
12
24, 36, 60input numbers•
3 integerscount
Find the Greatest Common Divisor (GCD) 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 Greatest Common Divisor (GCD)?+
The Greatest Common Divisor (GCD), also known as Highest Common Factor (HCF), is the largest positive integer that divides two or more numbers without leaving 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 of more than two numbers?+
Yes. Separate 3 or more integers using commas or spaces to find their common GCD.
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