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What is the greatest value of y such that 2^y is a factor of 11! ?

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What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 08 Dec 2016, 12:58
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E

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Question Stats:

73% (00:30) correct 28% (00:22) wrong based on 59 sessions

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Kudos [?]: 132525 [0], given: 12324

Director
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Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 08 Dec 2016, 20:07
Bunuel wrote:
What is the greatest value of y such that 2^y is a factor of 11! ?

A. 3
B. 5
C. 6
D. 7
E. 8



11/2=5
11/2^2=2
11/2^3=1

we will not calculate 11/2^4 as 2^4>11

total= 5+2+1=8

Ans E

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Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 09 Dec 2016, 00:12
Option E)

\(\frac{11}{(2^1)} = 5\)
\(\frac{11}{(2^2)} = 2\)
\(\frac{11}{(2^3)} = 1\)

Y \(= 5 + 2 + 1 = 8\)
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Kudos [?]: 58 [0], given: 90

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Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 09 Dec 2016, 00:32
Greatest value of y such that 2^y is a factor of 11!

11! = 1*2*3*4*5*6*7*8*9*10*11 which is same also 11! = 1*2*3*2*2*5*2*3*7*2*2*2*9*2*5*11

Count all occurrence of 2 in the expression = 8

The largest power of 2 that will still result in a factor of 11! is 2^8

Kudos [?]: 1 [0], given: 7

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Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 09 Dec 2016, 00:34
Greatest value of y such that 2^y is a factor of 11!

11! = 1*2*3*4*5*6*7*8*9*10*11 which is same also 11! = 1*2*3*2*2*5*2*3*7*2*2*2*9*2*5*11

Count all occurrence of 2 in the expression = 8

The largest power of 2 that will still result in a factor of 11! is 2^8

Ans E

Kudos [?]: 1 [0], given: 7

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Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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New post 12 Dec 2016, 18:14
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Bunuel wrote:
What is the greatest value of y such that 2^y is a factor of 11! ?

A. 3
B. 5
C. 6
D. 7
E. 8


To determine the number of factors of 2 within 11!, we can use the following shortcut in which we divide 11 by 2, and then divide the quotient of 11/2 by 2 and continue this process until we can no longer get a nonzero integer as the quotient.

11/2 = 5 (we can ignore the remainder)

5/2 = 2 (we can ignore the remainder)

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 11!.

Thus, there are 5 + 2 + 1 = 8 factors of 2 within 11!.

Answer: E
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Kudos [?]: 900 [1], given: 5

Re: What is the greatest value of y such that 2^y is a factor of 11! ?   [#permalink] 12 Dec 2016, 18:14
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