How this calculator works
A number divides every list entry exactly when it divides their greatest common factor. The smallest non-trivial divisor of that GCF must be prime: a composite divisor would itself have a smaller divisor. The step table shows the GCF after each list entry. Negative signs are ignored; a zero entry imposes no additional restriction when another entry is non-zero. Inputs are limited to 15 integers of magnitude at most one trillion.
Formula
g=gcd(|n₁|, |n₂|, ...). If g=1 there is no shared divisor above 1; otherwise the answer is the smallest prime divisor of g.
Worked example
For 45, 75 and 105, the running GCF is 45, then 15, then 15. The smallest prime dividing 15 is 3, so the least common factor greater than one is 3.
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Frequently asked questions
Is the least common factor always 1?
If 1 is allowed, yes. The non-trivial version used here explicitly excludes it.
Is this the least common multiple?
No. A common factor divides the inputs; a common multiple is divisible by the inputs.
What happens for coprime numbers?
Their GCF is 1, so the tool reports that there is no common factor greater than 1.