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If 25*24*23 ... 3 * 2 * 1 is expanded, how many zeros are there at the end of the answer? 

is there some shortcut to solve this? 

 May 6, 2021
 #1
avatar+121055 
+3

Here's  the  shortcut :

 

25*24*23* .....* 2 * 1   =  25!

 

Divide  25  / 5    and discard  any  remainders =   5

 

Divide 25 / 5^2    and discard any remainders =   25  /  25  =  1

 

Add  the  whole  numbers  =   5 + 1  =  6 trailing zeroes

 

Another  example

 

300!

 

300 / 5   =    60

 

300/5^2   =   300/ 25   =  12

 

300/5^3 =   300/125  =  2  + 50/125

 

Add the whole numbers =   60 + 12 + 2    =   72 trailing zeroes

 

 

 

 

cool cool cool

 May 6, 2021
 #2
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thank you so much!! this helped a lot, as well as the extra example. 

Guest May 6, 2021

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