Class number

In number theory, the class number is a way to measure how unique the way numbers can be broken down into prime factors within a particular number system called a *number field*. It indicates how many different "ideal classes" there are, reflecting the failure or success of unique factorization (like how every number factors uniquely into primes in regular integers). A class number of 1 means every number factors uniquely, similar to ordinary integers. Higher class numbers indicate more complexity and fewer unique factorizations, revealing deeper properties of the number field’s structure.