Posted by **Jon** on Monday, July 30, 2012 at 11:10am.

What is the smallest number n such that n! ends in at least 1000 zeros in base 10 notation

- math -
**Steve**, Monday, July 30, 2012 at 11:52am
you need 10 to be a factor 100 times.

That means you need 2^100 and 5^100 to be factors.

If [n] is the greatest integer <= n,

n! has 5 as a factor [n/5]+[n/25]+[n/125]+... times.

So, solve [n/5]+[n/25]+[n/125]+[n/625]+[n/3125] = 1000.

if n=4005,

[4005/5]+[4005/25]+[4005/125]+[4005/625]+[4005/3125]

= 801+160+32+6+1 = 1000

Naturally, 2 occurs as a factor many more times than this, so 4005! is the first factorial to end in 1000 zeros.

## Answer this Question

## Related Questions

7th grade, math - Can someone explain the steps to solve this problem? If a ...

math - If the digits of a number may be any one of 0 through 9 (except the first...

math - If the digits of a number may be any one of 0 through 9 (except the first...

math - If the digits of a number may be any one of 0 through 9 (except the first...

math - ) A wierd number is a number that is the product of two consecutive ...

Homework help plz( Steve or Reiny) - Determine if the number is written in ...

math - what is the least common denominator? It is the smallest number into ...

Math - Write 27 as a number is base five. The number 1000^2 is what in base ten...

Math - Please show your solution and how you did it. Thank you so much. 1.If x ...

maths - How many positive integers N are there such that the least common ...