Question

Find the maximum value of n such that 50! is perfectly divisible by ${2520}^n$.

• A. 6
• B. 8
• C. 7
• D. None of these

Answer 1

The correct option is B 8

$2520=7\times 3^2\times 2^3\times 5$
The value of n would be given by the value of the number of 7s in 50!
This value is equal to $\left[\frac{50}{7}\right]+\left[\frac{50}{49}\right]=7+1=8$
Option (b) is correct.