Question 25
For every integer $n\ge2,$ let $\operatorname{pow}(n)$ be the largest power of the largest prime that divides $n.$ For example, $\operatorname{pow}(144)=\operatorname{pow}(2^4\cdot3^2)=3^2.$ What is the largest integer $m$ such that $2010^m$ divides $$
\prod_{n=2}^{5300}\operatorname{pow}(n)?
$$
\prod_{n=2}^{5300}\operatorname{pow}(n)?
$$