10^999 = 2^999 x 5^999

10^998 = 2^998 x 5^998

now 10^999 will be divisible by 2^0 x 5 ^999 but not 10^998, similarly 2^1 x 5^999 , 2^2 x 5 ^999 .............. thus there will be thousand +ve integers

similarly we can do for 2^999 x 5^0 .....  it will have 999 nos since 2^999 and 5^999 are already counted in above.

thus 1999 factors

also we can calculate no . of factors of both then calculate the difference:

i.e. (999+1)(999+1) - (998+1)(998+1) = 1999

So the number is 1999