Greatest Common Factor Calculator

The tool computes the greatest common factor (GCF) of two or more integers using the Euclidean algorithm. It accepts negative inputs and zeros, returning a non-negative gcd that equals the gcd of the absolute values. Conceptually, the gcd is the largest integer that divides every input without remainder. The primary use is educational and algorithmic: verify homework answers, preprocess data, or support gcd-based logic in software. Under the hood, the implementation reduces the problem by pairwise gcd and aggregates results across all inputs, ensuring deterministic outcomes for any valid integer set. The approach scales with input size, and for many numbers the operation remains efficient due to the logarithmic complexity of the Euclidean method. The tool focuses on gcd value rather than full factorization, though prime-factorization can be offered as an enhancement in a future version. Use cases include classroom practice, competitive programming prep, and data normalization tasks where common divisors matter.