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In how many zeros does 75! end? (Note that $n!$ is the product of the first $n$ positive integers; for example, $5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120$.)

Dabae  Jul 7, 2015

Best Answer 

 #1
avatar+88751 
+10

There is an algorithm for this.....

 

Note that a zero is added everytime a "5" is multiplied by an even number....so....we just need to find the number of 5s that are multiplied in 75!

 

Divide 75 by 5 =   15

 

Divide 75 by 5^2   =   75  / 25   = 3

 

Then...there are 15 + 3  = 18  "5s" that are multiplied together in 75!......and we have more than enough even numbers to pair each 5 with....so......

 

Add 15 + 3     = 18 trailing zeros

 

 

CPhill  Jul 7, 2015
 #1
avatar+88751 
+10
Best Answer

There is an algorithm for this.....

 

Note that a zero is added everytime a "5" is multiplied by an even number....so....we just need to find the number of 5s that are multiplied in 75!

 

Divide 75 by 5 =   15

 

Divide 75 by 5^2   =   75  / 25   = 3

 

Then...there are 15 + 3  = 18  "5s" that are multiplied together in 75!......and we have more than enough even numbers to pair each 5 with....so......

 

Add 15 + 3     = 18 trailing zeros

 

 

CPhill  Jul 7, 2015

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