How this calculator works
A list GCD applies the two-number operation repeatedly. Once the running result reaches one, no later entry can increase it. Every positive divisor of the final GCD divides every input, so the common-divisor list is complete. The alternative views show the positive divisors or prime factors of each magnitude. Factor lists and trial division are bounded by the stated input limit to keep the work manageable.
Formula
gcd(a,b,c) = gcd(gcd(a,b),c). In prime factorization, retain only primes shared by every non-zero entry and choose the smallest exponent for each. Positive common divisors are exactly the divisors of the GCD.
Worked example
24 = 2³ × 3, 36 = 2² × 3² and 60 = 2² × 3 × 5. Their shared factors give 2² × 3 = 12. The common positive divisors are 1, 2, 3, 4, 6 and 12.
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Frequently asked questions
Does greatest common denominator mean the same thing?
It is sometimes used informally for GCD, but greatest common divisor is clearer. A common denominator for fractions is instead a common multiple of their denominators.
Do negative signs affect the GCD?
No. A positive divisor divides an integer exactly if and only if it divides its absolute value. The factor views therefore use magnitudes.
Can the list include zero?
Yes. Every positive integer divides zero, so zeros leave the GCD of the other entries unchanged. A list containing only zeros is rejected.