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What is the greatest value of x such that 2^x is a factor of 8! ?

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Bunuel
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What is the greatest value of x such that 2^x is a factor of 8! ? [#permalink] New post   08 Dec 2016, 12:55
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What is the greatest value of x such that 2^x is a factor of 8! ?

A. 9
B. 8
C. 7
D. 5
E. 3
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C
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rohit8865
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Re: What is the greatest value of x such that 2^x is a factor of 8! ? [#permalink] New post   08 Dec 2016, 19:40
Bunuel wrote:
What is the greatest value of x such that 2^x is a factor of 8! ?

A. 9
B. 8
C. 7
D. 5
E. 3



8/2=4
8/2^2=2
8/2^3=1

thus 4+2+1=7

Ans C
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Re: What is the greatest value of x such that 2^x is a factor of 8! ? [#permalink] New post   10 Dec 2016, 02:00
Bunuel wrote:
What is the greatest value of x such that 2^x is a factor of 8! ?

A. 9
B. 8
C. 7
D. 5
E. 3

The greatest value of x such that 2^x is a factor of 8! is -

8/2 = 4
4/2 = 2
2/2 = 1

So, The greatest value of x such that 2^x is a factor of 8! is (C) 7
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Re: What is the greatest value of x such that 2^x is a factor of 8! ? [#permalink] New post   12 Dec 2016, 18:04
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Bunuel wrote:
What is the greatest value of x such that 2^x is a factor of 8! ?

A. 9
B. 8
C. 7
D. 5
E. 3


To determine the number of factors of 2 within 8!, we can use the following shortcut in which we divide 8 by 2, and then divide the quotient of 8/2 by 2 and continue this process until we can no longer get a nonzero integer as the quotient.

8/2 = 4

4/2 = 2

2/2 = 1

Since 1/2 does not produce a nonzero quotient, we can stop.

The final step is to add up our quotients; that sum represents the number of factors of 2 within 8!.

Thus, there are 4 + 2 + 1 = 7 factors of 2 within 8!.

Answer: C
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Re: What is the greatest value of x such that 2^x is a factor of 8! ? [#permalink]
12 Dec 2016, 18:04
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