How many zeros are there at the end of 100!?

[Bellweather]

That is, 100 factorial. It's a homework question, anybody know a good way of going about this?

 

[milehigh]

Microsoft Excel:

=FACT(100)

9.3326E+157

 

[geno]

"7!"
"No dad, it's a rhetorical question"
"Rhetorical eh? .... 8!"
"Do you know what rhetorical means?"
"Do I know what rhetorical means?" 😀

 

[crackersjacks]

I think it's 24 but I'm not positive. Don't know how to do it mathematically though. Wrote a C++ program a while back for some class and it just so happens to do factorials.
100!=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 perhaps

 

[MikeO]

<< "7!"
"No dad, it's a rhetorical question"
"Rhetorical eh? .... 8!"
"Do you know what rhetorical means?"
"Do I know what rhetorical means?" 😀 >>



LOL 😀

Yep, that's me if I ever have kids 😱 😉

 

[SaltBoy]

<< I think it's 24 but I'm not positive. Don't know how to do it mathematically though. Wrote a C++ program a while back for some class and it just so happens to do factorials.
100!=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 perhaps >>



How many digits is that?! :Q

<edit> Nevermind -- 159, I believe

 

[nukefarmer]

Ask Dr. Math

 

[crackersjacks]

Bellweather, do you just have to show the answer or do you have to do something to prove it? What kind of homework assignment is it for what kind of class?
Sweet, Dr. Math likes my answer of 24 it seems.
Great link btw nukefarmer.

 

[cavingjan]

Lookat it from a more practical standpoint. How many combinations in the factorial are going to produce a multiple of 10? Go in some order: a multiple of 10 with any number will give a 0 at the end (so that is 11; 100 counts as 2). A multiple of 5 (that is not a multiple of 10) will produce a 0 at the end with any given even number (another 10). Are there any other number combinations other than the ones mentioned that will arrive at a number ending in a 0? What I have listed makes it a minimum of 21. Find the other 3.

 

[guyver01]

100! =
93,326,215,443,944,200,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.00


start counting 😉

 

[yakko]

What is this math stuff you speak of?

 

[NelsonMuntz]

The number is:
933262154439442.0E+143
and the rest of the digits are zeroes, so there are 143 zeroes at the end of 100!.

 

[Bellweather]

It's for a discrete mathematics class, and I'm just not sure how they want us to go about it. I think it would be good, although time consuming, to exapand each number of the factoria, 1 through 100 into its prime factorization, like 100 = 2^2 x 5^2, and 98 = 2^1 x 7^2, and keep multiplying all the factors of 10 that I can find. Maybe there is a simpler way. I could assume doctor math is right, and copy his thought process, but... (Good link though).

 

[natto fire]

here ya go
93326215443944200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.00
Enjoy!

 

[Bellweather]

I've seen two votes for 143 zeroes. Do either of you have any justification? I'd be interested to here it if you do. I'm not quite sure where doctor math concludes that every number that ends in a 5 results in another zero. Anybody want to give some insight?

 

[crackersjacks]

Another vote for 24
Check here as well, it backs up Dr. Math's answer.

 

[juiio]

It is not 143. You aren't seeing all the digits. The rest aren't all 0. The correct answer is 24.

 

[juiio]

<< I've seen two votes for 143 zeroes. Do either of you have any justification? I'd be interested to here it if you do. I'm not quite sure where doctor math concludes that every number that ends in a 5 results in another zero. Anybody want to give some insight? >>



Sure. 5 times an even number results in a number htat ends in 0. Example: 5*2=10, 15*12=180, etc.

Numbers that are 5^2 * n count for two. Example: 25*4 = 100, which is two zeroes. 50*2=100, 75*4, etc

Along the same lines, if you went high enough, 5^3 * n would count as three. Example: 125*8=1000