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If 7^n is a factor of the product of the integers from 1 to 100, inclu

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Bunuel
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If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  26 Apr 2016, 01:01
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E

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If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?

A. 12
B. 13
C. 14
D. 15
E. 16
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Re: If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  26 Apr 2016, 03:38
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Product of the integers from 1 to 100 = 100!

Number of 7's in 100! = 100/7 + 100/7^2 = 14 + 2 = 16

Answer: E
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arirux92
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Re: If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  26 Apr 2016, 03:29
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Bunuel wrote:
If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?

A. 12
B. 13
C. 14
D. 15
E. 16



So the question just means that we have to find all the multiples of 7 between 1 to 100

So

So there are 14 multiples of 7 ( 7 - 98)

But 49 and 98 contain two 7's as factors

so we have to add 14 + 2 = 16

E
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sudhirmadaan
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Re: If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  26 Apr 2016, 22:19
arirux92 wrote:
Bunuel wrote:
If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?

A. 12
B. 13
C. 14
D. 15
E. 16



So the question just means that we have to find all the multiples of 7 between 1 to 100

So

So there are 14 multiples of 7 ( 7 - 98)

But 49 and 98 contain two 7's as factors

so we have to add 14 + 2 = 16

E


calculation may get wrong some time, check out this easy concept and its implementation

everything-about-factorials-on-the-gmat-85592.html
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Abhishek009
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Re: If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  27 Apr 2016, 09:13
Bunuel wrote:
If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?

A. 12
B. 13
C. 14
D. 15
E. 16


Quote:
product of the integers from 1 to 100, inclusive


Means 100!

Quote:
7^n is a factor of the product of the integers


So, The problem condenses number of 7 in 100!

No of 7 in 100 ! is

100/7 = 14
14/7 = 2

So, Total number of 7 in 100! is 16

Answer will be (E)
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Re: If 7^n is a factor of the product of the integers from 1 to 100, inclu [#permalink] New post  06 Feb 2023, 02:33
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