Mathematics
OpenStudy (anonymous):

How many zeros at the end of 1000!

OpenStudy (anonymous):

NO NO NO

OpenStudy (anonymous):

noo

OpenStudy (anonymous):

1000! is a super large number

OpenStudy (anonymous):

?

OpenStudy (anonymous):

wut?

OpenStudy (anonymous):

yah im confused

Parth (parthkohli):

1000 * 999 * 998 * 997 ......... 1

OpenStudy (anonymous):

a ok lol

OpenStudy (anonymous):

zeros, as in the number of zeros in all the numbers up till 1000????

OpenStudy (anonymous):

1(0,0,0)

OpenStudy (anonymous):

249 zeros. Is this right?

Parth (parthkohli):

I see there's a method. The answer that comes for me is 248

OpenStudy (anonymous):

It is 249.

OpenStudy (anonymous):

200+40+8=248

Parth (parthkohli):

1000/5 + 1000/25 + 1000/125

Parth (parthkohli):

200 + 40 + 8 248

OpenStudy (anonymous):

OpenStudy (anonymous):

haha well like a lot, there's ten in every one hudred until you reach on hundred then there are 12 so 12 and 100 = 1200 I think?

OpenStudy (anonymous):

Elementary. This is given by Legendre's formula.

OpenStudy (anonymous):

wait 10, 20, 30, 40, 50, 60, 70, 80, 90 100 = 11 1000 x 11 = 11000 D: maybe?

OpenStudy (anonymous):

OpenStudy (anonymous):

thats not possible

OpenStudy (anonymous):

248.

OpenStudy (anonymous):

yeah that is what i got

OpenStudy (anonymous):

248

OpenStudy (anonymous):

To find the multiplicity of 5 in 1000!, use Legendre's Formula http://en.wikipedia.org/wiki/Factorial $\left\lfloor \frac{1000}{5}\right\rfloor +\left\lfloor \frac{1000}{5^2}\right\rfloor +\left\lfloor \frac{1000}{5^2}\right\rfloor +\left\lfloor \frac{1000}{5^3}\right\rfloor +\left\lfloor \frac{1000}{5^4}\right\rfloor =200+40+8+1= 249$ Of course the multiplicity of 2 is more than 249. 2 and 5 together generate zeros. There are 249 zeros.