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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 26 Apr 2016, 01:01
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

61% (01:03) correct 39% (01:26) wrong based on 592 sessions

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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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E
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If 7^n is a factor of the product of the integers from 1 to 100, inclu 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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If 7^n is a factor of the product of the integers from 1 to 100, inclu 26 Apr 2016, 03:29
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Bunuel
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
Show more


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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If 7^n is a factor of the product of the integers from 1 to 100, inclu 26 Apr 2016, 22:19
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arirux92
Bunuel
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
Show more

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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If 7^n is a factor of the product of the integers from 1 to 100, inclu 27 Apr 2016, 09:13
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Bunuel
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
Show more

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

Means 100!

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

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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If 7^n is a factor of the product of the integers from 1 to 100, inclu 10 Sep 2025, 12:17
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