Number of common divisors between two given numbers
I need to find the total number of divisors which divide both the numbers lets say N and M. Actually I tried to think about it a lot and searched at a lot of places for a possible answer. All I could think of was finding the prime factors and generating the actual divisors from the factors ? However this would take a lot of computation,therefore I need a much faster method performing much fewer operations? Is there any well known algorithm or formula for this problem or any derivable formula? I think the answer should be the number of divisors of the gcd of the 2 numbers.