Could you tell me the number of final zeros in the product of all the whole numbers between 100 and 200? I think the answers is 27 but I need some kind of external confirmation. thank you for your time

Guest Sep 18, 2017

#1**0 **

So are you asking for something like 200! but only to 100 and to determine the amount of zeros from the product?

c:

HighSchoolCalculus
Sep 18, 2017

#3**0 **

Yes to be fair I calculated the number of zeros in 100! and 200! and then I did the difference adding the two zeros for 100

Guest Sep 18, 2017

#4**0 **

How did you calculate the number of zeros in 200! Do you know that there is a trick to find the number of trailing zero in ANY number, such as 10^12! ?

Guest Sep 18, 2017

#5**+1 **

Number of zeroes from 100 to 200 [inclusive] =

Each multiple of "5" from 100 to 200 adds an additional "0" = 20

Each multiple of 25 from 100 to 200 adds another "0" = 4

Each multiple of 125 adds another "0" = 1

So..... we have 2 "0s" in 100 + 20 + 4 + 1 = 2 + 20 + 4 + 1 = 27

We can confirm this by evaluating 200! / 99! here : https://www.wolframalpha.com/input/?i=200!+%2F99!

CPhill
Sep 19, 2017