help a maths puzzle?

Question

In the following product, each alphabet represents an
unique single digit number,and * denotes a single digit
natural number. What is the value of F?

ABCDEFGH
X *
---------
FFFFFFFFF

Answer 1

FFFFFFFFF = F x 111111111

Factoring 111111111 gives

111111111 = 3^2 x 37 x 333667

So, the only one - digit divisors of FFFFFFFFF can be

1, 3, 9, F

and 3 x F if F=<3, which gives

3 if F = 1 (nothing new!)
6 if F = 2
9 if F = 3 (nothing new!)

and 9 x F if F = 1, which gives 9 (nothing new!)

We will examine all the cases
* = 1 => ABCDEFGH = FFFFFFFFF (not true, 8 digits on the left, and 9 on the right)

* = 3 => ABCDEFGH = 37037037 x F
Because ABCDEFGH =< 98765432, we have F =< 2
F = 1 => ABCDEFGH = 37037037 => F = 0 (not true!)
F = 2 => ABCDEFGH = 74074074 => F = 0 (not true!)

* = 9 => ABCDEFGH = 12345679 x F
Becaude ABCDEFGH =< 98765432, we have F =< 8
F = 1 => ABCDEFGH = 12345679 => F = 6 (not true!)
F = 2 => ABCDEFGH = 24691358 => F = 3 (not true!)
F = 3 => ABCDEFGH = 37037037 => F = 0 (not true!)
F = 4 => ABCDEFGH = 49382716 => F = 7 (not true!)
F = 5 => ABCDEFGH = 61728395 => F = 3 (not true!)
F = 6 => ABCDEFGH = 74074074 => F = 0 (not true!)
F = 7 => ABCDEFGH = 86419753 => F = 7 (TRUE!)
F = 8 => ABCDEFGH = 98765432 => F = 4 (not true!)

* = 6 => (F = 2) ^ ABCDEFGH = 37037037 => F=0 (not true!)

* = F => ABCDEFGH = 111111111 (not true, 8 digits on the left and 9 on the right)

So, the only solution is
86419753
x 7
--------------
777777777
Of course, we have asumed that F = 0. If F = 0, we must have * = 0 and every number of the form
ABCDE0GH
x 0
----------------
000000000

Answer 2

If *=0, then F=0

Answer 3

86419753*9=777 777 777

Answer 4

Puzzled toooooooooo