Find the least integer n such that n! is divisible by10^(6)

Question

Find the least integer n such that n! is divisible by
`10^(6)`

Answer 1

25!

in this type of questions you need to find 10 makers ( it's means you need to find numbers which has 2 or 5 in their prime factors) obviously there is a bunch of numbers which has 2 in their prime factors.

so we need to find multiples of 5. But you should be aware that some numbers have more than one prime factors of 5 e.g. 25 .

ok let's go back to the question.

starting from 1 , we've got 5, 10 , 15 ,20 &25(5²)

so the answer is 25!