The existence of this function for two elements of a ring ensures that the ring is a principal ideal domain. This value can be found by beginning a sequence with the two given numbers with the larger one first and repeatedly adding to the sequence with the difference between the second to last number and the largest multiple of the last number that will leave a positive re
The existence of this function for two elements of a ring ensures that the ring is a principal ideal domain. This value can be found by beginning a sequence with the two given numbers with the larger one first and repeatedly adding to the sequence with the difference between the second to last number and the largest multiple of the last number that will leave a positive result. That process is known as the Euclidean algorithm, and if this value is one for two numbers, then the numbers are said to be relatively prime. It can also be calculated by dividing the product of two numbers by their least common multiple. Given the prime factorization of two numbers, this value can be found by multiplying together the set of their common prime factors. Name this value which is the largest value that divides two numbers.
The existence of this function for two elements of a ring ensures that the ring is a principal ideal domain.
{greatest common factor} [or {greatest common divisor}; or {GCF}; or {GCD}]