Math Is Fun Forum

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Urgent help needed in factorial

Urgent help needed,obtain a number n such that n! has exactly 250  0's at right(if any).please show the method how you obtained n (or showed that there is no such n).

Last edited by {7/3} (2013-05-17 00:43:14)

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There are 10 kinds of people in the world,people who understand binary and people who don't.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Urgent help needed in factorial

hi

There'll be one zero for every factor of ten.

It's enough to count the factors of 5 as there are plenty of factors of 2 to spare.

So it's just a matter of considering the five times table.

0!      1 
1!      1
2!      2
3!      6
4!      24
5!      120  first zero here
6!      720
7!      5040
8!      40320
9!      362880
10!      3628800 number two here
11!      39916800
12!      479001600
13!      6227020800
14!      87178291200
15!      1307674368000

Note:  when you get to factorial 25 this puts in two fives so there are 6 zeros at this point.

Similarly, 50, 75 and 100 give an extra zero.

There's another jump at 125! and so on.  You'll have to allow for the multiples of powers of five.

I'll check your answer if you wish to post back.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent help needed in factorial

Hi;

There are 2 nice facts known about the problem.

The number of trailing zeros is given by

1000! has 249 zeros.

You need to try from there and you find one quickly. Obvious from the formula it is ...

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Urgent help needed in factorial

I'm getting 1005,1006,1007,1008,1009.Are these correct?

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There are 10 kinds of people in the world,people who understand binary and people who don't.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent help needed in factorial

Hi;

Yes, that is correct.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Urgent help needed in factorial

hi {7/3}

That's what I got too. 

Bob

http://www.wolframalpha.com/input/?i=1005%21

Keep clicking for more digits until you get them all.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob