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Question

Answer 1

+4 A:

floor(n/5) + floor(n/25) + floor(n/125)+.......+floor(n/5^n)

in your case n = 41

See comments below

Sorantis 2010-03-19 23:59:41

Surely you mean floor()?

Simon Nickerson 2010-03-20 00:01:56

round here shows that only integer part of each expression should be considered (yes, floor)

Sorantis 2010-03-20 00:04:11

@Sorantis: `round(9/5) = 2` and `floor(9/5) = 1`

N 1.1 2010-03-20 00:06:27

see comment above

Sorantis 2010-03-20 00:07:13

n=41, not 9 ... (9/5) was just an example for demonstrating floor vs. round

tanascius 2010-03-20 00:13:33

The result IS 9

Sparr 2010-03-20 00:40:56

ok, i've understand all! thanks

Syom 2010-03-20 00:56:56

Answer 2

+7 A:

If you know the trick, you don't even need paper. The number of zeros at the end is how many times it's divisible by 10 . . . in terms of the prime factorization, this is the minimum of the number of times it's divisible by 5 and the number of times it's divisible by 2 (since we need one factor of both 2 and 5 to make a factor of 10). But with factorial we're including every factor less than or equal to 41, so we'll get a lot more factors of 2 than factors of 5. So we only need to worry about how many factors of 5 there are.

So count the numbers that are less than or equal to 41 and divisible by 5: 5,10,15,20,25,30,35,40

There's 8 of them, but don't forget that 25 gives us an extra factor of 5, since it's divisible by 5 twice. So 9 factors of 5 (and thus 9 factors of 10) in all.

Tim Goodman 2010-03-20 00:21:20

+1 This is *so* much clearer than the Sorantis thread.

Jon-Eric 2010-03-20 00:30:00

Good explanation. I just wrote the result of it in one formula. I thought it was pretty obvious. My bad

Sorantis 2010-03-20 00:33:25

@Syom, it mean that you didn't really understand the question you were asked. And coming back to your question it means that there's 49 digits more, written in scientific format.

Sorantis 2010-03-20 00:35:12

@Syom: That's scientific notation . . . it means 3.345... times 10 to the 49th power. But often with scientific notation some of the digits are truncated. In this case the exact answer is 33452526613163807108170062053440751665152000000000, or in other words 3.3452526613163807108170062053440751665152 x 10^49 [Source: WolframAlpha -- just type in 41! (the ! means factorial)]

Tim Goodman 2010-03-20 00:36:42

However, don't go turning that answer in . . . the point of the problem is surely to understand the factorization so you don't *have* to actually compute 41!

Tim Goodman 2010-03-20 00:38:06

@Tim Goodman you are really goodman:))))))))))) thanks

Syom 2010-03-20 00:42:05

@Syom: You're welcome.

Tim Goodman 2010-03-20 01:01:14

@Syom: I'm a little hesitant to post my contact info on a public forum, and unfortunately StackOverflow doesn't currently support private messaging. I'll keep replying to comments here if you want to discuss further . . . or if you have a followup question that's pretty far from this one perhaps it deserves its own topic.

Tim Goodman 2010-03-20 01:56:31

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