Find how many solutions (divisibility question)

There is an integer 27*36*5 where the asterisks are also numbers, you just don't know them. This number is divisible by 225. How many integer solutions does it have (not negative)

This is a follow up question to another one which was find a number such that *676* can be divided by 72. Found 2 different solution by brute force (there were only 45 things to pick from)

I don't understand how it is a follow up method. Is there a technique or method involved because I probably missed it in using brute force.

Please help if you can.