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# In how many zeros does 75! end? (Note that is the product of the first positive integers; for example, .)

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In how many zeros does 75! end? (Note that  is the product of the first  positive integers; for example, .)

Dabae  Jul 7, 2015

#1
+92674
+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
+92674
+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