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# Number of final zeros in a product

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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
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### 5+0 Answers

#1
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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
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Yep. And 100 and 200 are both part of the product

Guest Sep 18, 2017
#3
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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
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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
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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
edited by CPhill  Sep 19, 2017

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