Result
Greatest common factor
GCF = GCD = HCF
Normalized input
Common factors
Bézout identity
Meaning
GCF · GCD · HCF
Greatest Common Factor Calculator
Find the greatest common factor of two or more integers. Large values stay exact with BigInt, and the calculator shows the Euclidean work instead of hiding the answer.
Supports negatives and zero. Up to 100 integers, each up to 500 digits.
Euclidean algorithm — shown step by step
What the GCF means
The GCF is the largest positive integer that divides every entered value with no remainder. “GCF”, “GCD” and “HCF” are common names for the same quantity.
Zero handling
gcd(a, 0) = |a|. If every input is zero, the GCF is undefined, so this calculator reports that case rather than inventing a value.
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