Enigma

The British science weekly New Scientist runs a puzzle every week. The current puzzle is this:

The letters of EIGHTMAN represent different digits. When representing a number, ENIGMA is the product of GGG and TTT. Furthermore, a six-digit number using the letters of ENIGMA in a different order is the product of GGG and HHH.

Please send in the number EIGHTMAN.

I think this should be fairly easily amenable to an exhaustive search. There are only 72 possibilities for GGG and TTT (each is a digit from one to nine and different so 9 × 8 combinations). I expect that this would produce several possibilities — there would need to be at least two.

Another way to solve it would be to simply try all the eight digit combinations for EIGHTMAN and look for a match.

Of course if you get an answer to the actual problem then don't tell me, tell the New Scientist and maybe you can win £15! — if you do win, remember you owe me a beer for my help :)