Trailing Zeroes

[Kirono23]

Who can solve this problem?

 

[pka]

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?

 

[Kirono23]

The answer is 24
Here is the solution

 

[pka]

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?

 

[Kirono23]

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??