Think of the number 10

No. Of factors of $10^{998}=999^{2}, 10^{999}=1000^{2}$ . So answer is $1000^{2}-999^{2}=1999$

The numbers will be of form $2^{999} \times 5^x$ or $2^x \times 5^{999}$ , for $x = 0, 1, 2, 3, \dots, 999$ . Adding up, such numbers, we get $1000 + 1000$ . But $2^{999} \times 5^{999}$ is counted twice. Therefore the answer is $1999$ .