Simple factorial

What is the smallest number n n such that n ! n! is divisible by 8208 8208 ?


The answer is 19.

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1 solution

Feathery Studio
Jul 16, 2015

The prime factorization of 8208 8208 is 2 4 × 3 3 × 19 2^{4}\times3^{3}\times19 . Four multiples of 2 2 and three multiples of 3 3 can be obtained by 9 ! 9! , but to get a multiple of 19, it has to be 19 ! \boxed{19!} since 19 19 is prime.

well done my friend :)

Abdeslem Smahi - 5 years, 11 months ago

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