2010 AMC 12B Problem 25

For every integer n\ge2, let \text{pow}(n) be the largest power of the largest prime that divides n. For example \text{pow}(144)=\text{pow}(2^4\cdot3^2)=3^2. What is the largest integer m such that 2010^m divides

\prod_{n=2}^{5300}\text{pow}(n)?

\textbf{(A)}\ 74 \qquad \textbf{(B)}\ 75 \qquad \textbf{(C)}\ 76 \qquad \textbf{(D)}\ 77 \qquad \textbf{(E)}\ 78

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