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How many zeros to the left of the decimal would the number 300! have?

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Bunuel
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How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   19 Jan 2017, 08:03
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How many trailing zeros would the number 300! have?

A. 81
B. 74
C. 72
D. 60
E. 30
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B
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AMahmoodi
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Re: How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   19 Jan 2017, 10:26
Hi is 74 correct:?:
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Re: How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   19 Jan 2017, 13:43
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Hi, I'm going with answer choice B: 74.

Here is my breakdown:

300/5 = 60

(300/5^2) = 12

(300/5^3) = 2

60 + 12 + 2 = 74. Therefore B.
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Re: How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   19 Jan 2017, 14:51
First I did not understood problem at all. Later within seconds I remember Bunuel Trailing Zero concept
300/5 = 60
60/5 = 12
12/5 = 2
or
300/5 + 300/25 + 300/125 = 60 + 12 + 2 = 74
B
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Re: How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   08 Jul 2020, 13:34
Bunuel

I think this question must be rephrased. As it is, we cannot assume that there are no other zeros in 300! except the trailing zeros

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How many zeros to the left of the decimal would the number 300! have? [#permalink] New post   12 Sep 2020, 19:55
To find the No. of Trailing Zeroes in 300! we need to find the Count of Factors Pairs (2*5) that exist in 300!

Since there will definitely be More Prime Bases of 5 than Prime Bases of 2, if we find how many Prime Bases of 5 exist in 300! ----- then this will lead us to how many Factor Pairs of (2*5) will exist that create the No. of Trailing Zeros


300/5 = 60

60/5 = 12

12/5 = 2

60 + 12 + 2 = 74

The Max Power of 5^n that Divides into 300! evenly is ------ (5)^74

there will be 74 Trailing Zeroes

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How many zeros to the left of the decimal would the number 300! have? [#permalink]
12 Sep 2020, 19:55
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