+0

# Really Big Number!

+1
121
2

What is the number of trailing zeros in (10^10)!!. Note that "!!" is the double factorial function. Please just give me a hint and I will do the homework! Ridiculous question by our teacher. I thank you for any help.

Sep 24, 2018

#1
+1

That is a very big number!! But, there is a method to your teacher's madness!! Since you are willing to do the homework, I will give you a hint and you finish the job!.

Take 10^10 and divide it by the powers of 5 as follows:

(10^10) / 5  +  (10^10) / 5^2  +  (10^10) / 5^3  +  ............+  (10^10) / 5^14.

Note: It is very important that you divide them one at a time and take the INTEGER PART ONLY. Disregard the fractional part. Once you calculate them all, then add them up and DIVIDE THE TOTAL BY 2. Again, if there is a fraction, disregard it and keep the integer part only. That should give you a lot of zeros!!. Good Luck.

Sep 24, 2018
#2
+1

If you don't make any mistakes, you should get:
sumfor(n, 1, 14, int((10^10)/5^n) = 2499999997 / 2 =1,249,999,998 zeros !!!.

Sep 25, 2018