Powers and Factors

We can rewrite $7^{9999} = 7 \times 7 \times ... \times 7 \times 7$ (9999 times).

As all of the prime factors are 7, the factors are $1, 7, 7^2, 7^3, ... 7^{9998}, 7^{9999}$ .

We can obviously exclude $1$ , leaving us with $9999$ factors.

The number of factors that are greater than the number $= 9999 -$ The number of factors that are less than or equal to the number.

We find that $7^7 < 1000000$ and $7^8 > 1000000$

Therefore: The number of factors that are greater than the number $= 9999 - 7 = \boxed{9992}$