Little Maths Puzzle

A friend shoed me this today and I though som of you might be interested.

Start with 1,000,000 and (this was really to be done on a calculator) you can use the buttons +, -, *, / and = as well as the digit 7 only.

You have to try to get to 7 in the lest number of ‘steps.’

Apparently he can do it in 4, but I could only manage 7 or 8 I think (can’t remember exactly how I went)

Something like:

1,000,000 - 777,777 = 222,223
222,223 - 77,777 = … (a few times)

… = 8
8 - 7 = 1
1 * 7 = 7 (!)

Anyone heard of this problem before or can see a neat solution?