\[1)\ 100 = 2 \cdot 2 \cdot 5 \cdot 5:\]
\[N = (2 + 1)(2 + 1) = 3 \bullet 3 = 9.\]
\[Ответ:\ \ 9.\]
\[2)\ 1000 = 2^{3} \cdot 5^{3}:\]
\[N = (3 + 1)(3 + 1) = 4 \bullet 4 = 16.\]
\[Ответ:\ \ 16.\]