I just solved this by trial-and-error.
I'm sure there's a formula to this, but here's my reasoning:
If it is not divisiable by 2, 3, 4 ,5 ,6 ,or 10, it really has to be divisiable by 7, because 7 is a prime number.
So I tried 777, but that is divisiable by 3.
Next I tried 707, and when divided by 2, 3 ,4 ,5 ,6, and 10 it did not come out as a whole number.
So I got 707. Hope this helps.