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# Number theory

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If 25*24*23 ...*13*12*11 is expanded, how many zeros are there at the end of the answer?

Mar 6, 2022

#1
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There will be as many zeros at the end of the answer as there are factors of 10

To find the number of factors of 10, find the number of factors that are 5

and the number of factors that are 2.

25  =  5x5

20  =  5x4

15  =  5x3

So, there are 4 factors of 5.

There are more than 4 factors of 2, so there are a total of 4 factors of 10.

Therefore, there will be four zeros at the end of the answer.

Mar 6, 2022
#3
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There are 4 factors of 5

25 = 5 x 5

20 = 5 x 4

15 = 5 x 3

There is also 27 factors of 2, meaning that there are 4 zeros at the end

Corrected... Thanks Guest!!!

BuilderBoi  Mar 6, 2022
edited by BuilderBoi  Mar 7, 2022
#4
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I think the poster meant: 25 x 24 x 23.........to 11 ONLY!! If that is the case then geno3141's answer is correct.

Guest Mar 6, 2022
#2
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floor[25/5]  +  floor[25/25] ==6 zeros as follows:

25! ==15,511,210,043,330,985,984,000,000

Mar 6, 2022