2021 AMC 12B Problem 7

Let N=34\cdot34\cdot63\cdot270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N?

\textbf{(A) }1:16 \qquad \textbf{(B) }1:15 \qquad \textbf{(C) }1:14 \qquad \textbf{(D) }1:8 \qquad \textbf{(E) }1:3

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.