+0

# Number of final zeros in a product

0
1200
5

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

Sep 18, 2017

#1
+1491
0

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

c:

Sep 18, 2017
#2
0

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

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

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! ?

Sep 18, 2017
#5
+124676
+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!

Sep 19, 2017
edited by CPhill  Sep 19, 2017