Trailing Zeroes

Do you have a question about trailing zeros?
Here is a question I have used: How many trailing zeros does \(124!\) have?
Can you answer that?
 
The answer is 24
Here is the solution
 

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The answer is 28. SEE HERE
You can see that \(5^{28}\) is a factor of \(124!\)
Every trailing zero results from a factor of ten.
If we try \(125!\) the answer jumps to \(31\). WHY?
 
The answer is 28. SEE HERE
You can see that \(5^{28}\) is a factor of \(124!\)
Every trailing zero results from a factor of ten.
If we try \(125!\) the answer jumps to \(31\). WHY?
Sorry I made a mistake, in my answer instead of 20 it should be 24 as 24*5=120
That's make the answer 24+4=28
Silly mistake??
 
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