Question 59

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


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.

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