Problem Solving

neilcao wrote:a number is the product of x numbers, when the number's last 6 digits are 0 (000000), what\s the least value of x?

we are talking about integers here.

I think the question should have been " a number is the product of x consecutive positive integers and it's last 6 digits are 0. What is th least value of x?"

Solution:
We proceed to calculate minimum value of x! which has 6 zeros in the end.
This will give the minimum value of x.
Now, 6 zeros means we need 6 fives and 6 twos in x!.
Now 25! has 5, 10, 15, 20, and 25 as factors.
Also they are giving in total 6 fives.
Now there are many twos in 25!.
So 6 twos will combine with 6 fives to give 6 zeros in the end.
Hence the minimum value of x is 25.