- 24 Apr '14 11:06 / 1 edit

1000 factorial. I can't even get an answer in my HP calculator, it only goes up to 500!.*Originally posted by talzamir***How many zero's are at the end of 1 x 2 x 3 x .... x 1,000 ?**

What's the non-zero number right before them?

I assume therefore there is a shortcut, but no idea what that would be.

My casio poops out at 69!, which is 1.7 E98, so only up to 2 digit exponent and my HP I think only has 3 digit exponents.

So the answer must be 248 zero's.

I cheated

http://voices.yahoo.com/the-number-zeros-end-1000-1000-factorial-888411.html - 24 Apr '14 12:11 / 1 editKinda funny that the answer you cheated from is wrong. ^_^

The principle is right, of course. The zeros at the end come from the 5's and the 2's when 1000 ! is factored, and since there are more 2's than 5's, it's enough to count the fives.

Yahoo noted correctly that every fifth number is divisible by five, so there are 200 fives. Every fifth of those is a multiple of 5^2 = 25 so those count twice; add 40 fives. Every fifth of those is a multiple of 5^3 = 125 so those count three times, add 8 more fives, for a total of 200 + 40 + 8 = 248, as yahoo claimed.

But they missed that 5^4 = 625 which is less than 1,000, which gives one more, for a total of 249, not 248. :-P

So.. what's the last non-zero number before the zeros start? - 24 Apr '14 16:28

Can't trust anyone anymore*Originally posted by talzamir***Kinda funny that the answer you cheated from is wrong. ^_^**

The principle is right, of course. The zeros at the end come from the 5's and the 2's when 1000 ! is factored, and since there are more 2's than 5's, it's enough to count the fives.

Yahoo noted correctly that every fifth number is divisible by five, so there are 200 fives. Every fifth of those ...[text shortened]... for a total of 249, not 248. :-P

So.. what's the last non-zero number before the zeros start?

How many digits total are there in 1000!? - 29 May '14 17:27

Please stop it! PLEASE! My brain is about to explode! Where's my duct tape?*Originally posted by talzamir***There are 2,568 of them as 1,000! = 10^2,567.605 = 4.02387 x 10^2,567.**

The number exists online, but was simply enough to check with excel by taking a 10-base log of 1..1000 and adding them together.

GRANNY.