Guest

Find the largest number n such that (2012!)! is divisible by ((n!)!)!.........where n! is the product of 1st n positive integers.

Find the largest number n such that (2012!)! is divisible by ((n!)!)!.........where n! is the product of  1st n positive integers.

Grade:10

1 Answers

kushal satya
37 Points
10 years ago

WE HAVE,

x! is divisible by r! if x>r.

this implies that

 

(2012!)! is divisible by ((n!)!)! if 2012!>(n!)!

this implies that

2012>n!

the greatest value of n which satisfies it is 6.


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free