What is the largest integer \(n\) such that \(7^n\) divides 1000! and the answer isn't 163
What is the largest integer \(n\) such that \(7^n\) divides \(1000!\)
\(\text{The largest integer $= \left[\dfrac{1000}{7}\right] + \left[\dfrac{1000}{7^2}\right] + \left[\dfrac{1000}{7^3}\right] \qquad [\ldots] =$ integer part. } \\ \text{The largest integer $= 142 + 20 + 2 $} \\ \text{The largest integer $= 164 $} \)