For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is
Select an option to reveal the answer and explanation

Question

For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is

Accepted Answer

7. To find the largest possible value of n, we need to find the value of n such that n! is less than 15000. 7! = 5040 8! = 40320 > 15000 This implies 15000! is not divisible by 40320! Therefore, maximum value n can take is 7. The answer is option B.