2021 Fermat Problem 25

Let N be the number of triples (x,y,z) of positive integers such that x < y < z and xyz = 2^2 \cdot 3^2 \cdot 5^2 \cdot 7^2 \cdot 11^2 \cdot 13^2 \cdot 17^2 \cdot 19^2. When N is divided by 100, the remainder is

\textbf{(A)}\ 28\quad \textbf{(B)}\ 88\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 68\quad \textbf{(E)}\ 48

If there are no answer choices shown, enter a numerical answer.

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