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how many zeros would 50! have and why?

 Oct 2, 2014

Best Answer 

 #1
avatar+128707 
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It would have 12......to see why....note that there are 10 multiples of 5 in 50! that could be paired with 10 even numbers in the product of 50! to produce a "0"  with each pairing. But 25 and 50 each have an additional factor of  "5" that could be paired with two other even numbers in the product of 50! ......so that gives us 12 trailing zeroes.

Note that there are 25 pairs of even numbers in the product of 50!, so we will be guaranteed to be able to pair twelve "5's with any twelve of them to produce 12 trailing zeroes.....!!!!

 

 Oct 2, 2014
 #1
avatar+128707 
+8
Best Answer

It would have 12......to see why....note that there are 10 multiples of 5 in 50! that could be paired with 10 even numbers in the product of 50! to produce a "0"  with each pairing. But 25 and 50 each have an additional factor of  "5" that could be paired with two other even numbers in the product of 50! ......so that gives us 12 trailing zeroes.

Note that there are 25 pairs of even numbers in the product of 50!, so we will be guaranteed to be able to pair twelve "5's with any twelve of them to produce 12 trailing zeroes.....!!!!

 

CPhill Oct 2, 2014

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