Greatest common divisor

[matqkks]

What are the advantages of using Euclid's algorithm over prime decomposition to find the gcd of two numbers?
Should you use Euclid’s algorithm in some cases and prime decomposition in others?

 

[I like Serena]

What are the advantages of using Euclid's algorithm over prime decomposition to find the gcd of two numbers?
Should you use Euclid’s algorithm in some cases and prime decomposition in others?

Euclid's algorithm is computationally cheaper than prime decomposition.
Prime decomposition is computationally hard, so the only reason to do it, is if the prime decomposition is needed for something else.
In comparison Euclid's algorithm takes a negligible amount of effort. So it can basically be done for free even if prime decomposition is needed for something else.