In how many zeros does 40!/(4 (5!)) end?

[kavitha]

In how many zeros does 40!/(4 (5!)) end?

 

[galactus]

How many multiples of 5 are between 1 and 40?

5, 10, 15, 20, 25, 30, 35, 40

Plus one more because we have 5x5=25.

So, there are 9 trailing 0's on 40!.

But, \(\displaystyle 4\cdot 5!=480\)

This 0 must be subtracted off.

Thus, there are 8 trailing 0's on \(\displaystyle \frac{40!}{4\cdot 5!}\)

 

[kavitha]

Hi galactus,
Can you please explain me. I couldn't catch up with the solution of 9 zeros.
Please guide me.

 

[galactus]

I just done some googling and found this. Perhaps it will help explain why this works better than I can:

http://www.purplemath.com/modules/factzero.htm

 

[kavitha]

Thanks, Now I get it. I can do for any number. Thanks again.

 

[pka]

In how many zeros does 40!/(4 (5!)) end?

Here is a neat trick. http://www.wolframalpha.com/input/?i=factor+40!
Look at the exponent on the factor 5. That tell us the number of trailing zeros in 40!

Change 40 to 125. You see that 125! will have 31 trailing zeros.

 

[mmm4444bot]

Perhaps it will help explain why this works better than I can

Gosh, Cody. You seem to work okay. :wink: