How to determine the key given the hash and input data?

Question

Encryption

Hello, do not scold. Help would be welcome.
There is, in general, a game. The game has a pirated version of the game that allows you to play online servers, but with one caveat.
This nuance is a serial key generator (aka hashes) for multiplayer. The brightest minds of this game gathered together and decided to figure out how this generator works. In general, when using it, the same serial number is generated, which is driven into the registry.
This serial looks extremely tasteless (ECACD9E1E4078EC3F41B2229616352C7DF3F84C2AE87C169B47F0FB846ECBFF1) - but its appearance is not important to us. What is the point, sobsna - when I enter the game server, I get a game ID. By the way, here it is (5545160).

I just can’t understand and feel how, on the basis of the game ID, this rubbish called the serial key is generated. It was not possible to determine the hash type, and if I confuse the terms somewhere, please forgive me.

And in short, this is what we have - input data (5545160) and hash (ECACD9E1E4078EC3F41B2229616352C7DF3F84C2AE87C169B47F0FB846ECBFF1). How to find the generation key of this hash?