Simple GCD utility in Java
Instead of throwing an Error, an AssertionError would be better.
An Error is too broad.
An AssertionError conveys better that instantiating is an error by the programmer, violating a precondition.
(The only way this error will be triggered is if you try to create an instance within this class.)

private GCD() {
    throw new AssertionError("Instantiation not allowed.");
}


As this class has only private constructors,
it cannot be extended:
derived classes would need to call a constructor in the super-class,
but none are available.
To make the intention perfectly clear that this class is not designed to be extended, it's good to make it final.