1000! how many trailing zeros?
Find the trailing number of zeros of 1 0 0 0 ! .
Notation: ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 .
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4 solutions
nice solution @Anh Khoa Nguyễn Ngọc
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Glad you like it! I have more of this kind here and here .
nice. where can i get infos that it is ≈ n / 4
@Anh Khoa Nguyễn Ngọc , as like all other functions, you should use a backslash as \log lo g so that it is not in italic which is for variables and constants. Note that log 5 l o g 5 has no space between log and 5 but \log 5 lo g 5 has. Use \left \lfloor \dfrac n5 \right \rfloor ⌊ 5 n ⌋ so that the floor function brackets are of the right size.
Easy problem,
I guess this would help you :)...
a website asked how many zeros (4.2 mil)! has.
it took me a while to understand why just dividing by 5 is not enough.
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I had posted a note, Can you answer that as I am doing a community poll, of a particular thing. The note would be present in the most recent ones...
What do you mean to say?
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just what is said: i m old and slow. u are young and fast.
how did u know the answer that fast?
maybe u can help with this other problem: i want to have the answers in ascending order.
do u know how to do that?
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Yeah sure, send the link, of the problem, I wasn't trying to demean you, sorry for my above comment.
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@Dibyojyoti Bhattacharjee – when i was creating this problem, i had the answers in ascending order, but it seems brilliant scrambles them. do u know how to keep the order ?
@Dibyojyoti Bhattacharjee
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@ Brilliant Mathematics
I tried to arrange the answers in ascending order but when I posted it, the order changed.
how to arrange the answers in the order that l want, when l post another problem?
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@Num Ic – No idea...
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@Dibyojyoti Bhattacharjee
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ty and sry. l was not aware that it creates that @ "you" too.
l will try out how to arrange the order when l post another problem.
but l want to avoid a long save-change-save chain. the preview has shown a different order than the final post.
@Num Ic – Hi num IC, we currently do not have that feature available to the public. Feel free to tag me and I will manually "unrandomize" the answer order.
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@Brilliant Mathematics
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ok. thank you for your offer.
it seems when l repeat it several times l get my prefered order. but l want to avoid a post-delete-post chain, to avoid confusing the other users.
does your correction interfere with the already given answers? if no: may l ask you to arrange the answeroptions for this question to ascending order?
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@Num Ic – Everytime you view a problem with multiple-choice-options, the options are always randomized, unless a staff has manually disabled it.
So every time you create a new community problem with multiple options, the options are always randomized.
If you need your problem's options to be unrandomized, just create a report under your problem, then tag me.
No, my correction does not interfere with the given options.
I've unrandomized the options for this problem of yours.
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@Brilliant Mathematics
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you are great. thank you very much and thank you for the info.
btw: i was delighted to see that two days ago this exact problem was chosen as daily problem. ;-)
I am not demeaning you, just wanted to say that the problem was easy.
ty for the pic. now i got what u mean.
Same way as @Dibyojyoti Bhattacharjee .
Btw bad handwriting
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yeah, bad handwriting rules you know ;)...
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No problem..
;-) bad handwriting indicates a genius (-;
you are a great programmer. it would be easy for you to use Latex.
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@Num Ic – Whom are you talking about? and what do you mean
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@Srijan Singh
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hm, i replied to a sub-post from Dibyojyoti, so i assumed it would be clear that i talk to him.
sry i still dont understand when i have to use the @ symbol.
@Num Ic – That's the bad part I don't know how to use latex, btw, I am posting a problem in an hour
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@Dibyojyoti Bhattacharjee – Wow new problem...
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@Srijan Singh – Problem uploaded
@Dibyojyoti Bhattacharjee – @Dibyojyoti Bhattacharjee i can give u a short example how to use Latex if u want.
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@Num Ic – Yeah Please.
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@Dibyojyoti Bhattacharjee – tell then.......
@Dibyojyoti Bhattacharjee
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@Dibyojyoti Bhattacharjee
lol, u already used it in your problem.
i knew u are fast ;-)
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@Num Ic – No he has not used latex in the problem it has been edited by the moderators because the way he has posted the problem was against the guidelines.
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@Srijan Singh – Yeah, I am not that fast...
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@Dibyojyoti Bhattacharjee – You're not fast but superfast
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@Srijan Singh – Are u flattering me?
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@Dibyojyoti Bhattacharjee – No bro I was just joking.
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@Srijan Singh – That's the spirit... Btw, u are from which state? No offense
@Dibyojyoti Bhattacharjee
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Latex code begins with: \
( and ends with: \)
to center it u can use: corner brackets: [ ] instead of round brackets: ( )
all text inside this brackets will be interpreted as Latex commands.
Numbers are just numbers, but
Latex commands begin with \
Example: to write 1/2 u can use \frac{1}{2} so it looks like:
2
1
you can just copy the next line and post it as a reply:
\
( \lfloor \frac{401}{2} \rfloor \approx 200 \)
then it should look like this:
⌊
2
4
0
1
⌋
≈
2
0
0
this side has very good and detailed infos: Latex guide 3.
If you would like to make friends from bengal you should interact with @foolish learner and @siddharth chakarvaty. @Dibyojyoti Bhattacharjee
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How is it possible??
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Just tag them in daily challenges and interact then they will know you're also from bengal
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@Srijan Singh – why shall I do that?
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@Dibyojyoti Bhattacharjee – I was just advising you to make friends.
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@Srijan Singh – No, I wanted to say why shall I tag unknown people...
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@Dibyojyoti Bhattacharjee – They're very known to brilliant just tag no problem
Use this .I solved this twice because he had edited once.
can u please post your solution again? i am curious how u solved it so fast.
Ok I will post in hour
1 0 0 0 : 5 = 2 0 0 ; 2 0 0 : 5 = 4 0 ; 4 0 : 5 = 8 ; ⌊ 8 : 5 ⌋ = 1 2 0 0 + 4 0 + 8 + 1 = 2 4 9
Nice...............
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I think it's you first problem
can u post your solution again? please?
There is also another technique. But since I cannot type so many mathematical symbols, so I cannot post the solution sorry for that @num IC .
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ok. if you explain it in words, i can try to write it down. is it about l o g 1 0 ?
Wait a minute, let me send a pic of the solution
For more practice solve this
Btw, @SRIJAN Singh , your problem was, easy. Is it a nsejs problem?
YEAH,I wanted to clear the concepts of @num IC in this.
Give something new in algebra or geometry...
@num IC .PLS edit the problem because you have written ! is faculty.It should be ! is factorial.
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Oh! now it has been edited.
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@SRIJAN Singh ty for the hint. but who did edit this?
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@Num Ic – Moderators
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@Srijan Singh – ty. it seems i have to check the guidelines before post another problem
Since the factors 5 and 2 are needed to make a trailing zero, we can take the floor function of how many times the powers of 5 divide n (since they are less common than powers of 2), I used this formula: i = 1 ∑ ⌊ lo g 5 n ⌋ ⌊ 5 i n ⌋
With n = 1 0 0 0 , we have 2 4 9 .
Or you can logically estimate the answer since i = 1 ∑ ⌊ lo g 5 n ⌋ ⌊ 5 i n ⌋ ≈ 4 n , so you would start guessing the answer.