> 2040 is, which is divisible by 7 iff 204 is

I don't follow that one.

To check whether 2747 is divisible by 7, I divide the multiple of 100 (i.e. 2700) by 50 (i.e. 54), add it to the remaining two digits, 47 (i.e. 101), then see if that's divisible by 7.