2021 AMC 10B Problem 12

Let N = 34 \cdot 34 \cdot 63 \cdot 270. 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.