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

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Math Expert
Joined: 02 Sep 2009
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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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08 Dec 2016, 12:58
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73% (00:30) correct 28% (00:22) wrong based on 59 sessions

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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
[Reveal] Spoiler: OA

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

Director
Joined: 05 Mar 2015
Posts: 963

Kudos [?]: 290 [0], given: 41

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

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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

Kudos [?]: 290 [0], given: 41

Manager
Joined: 18 Oct 2016
Posts: 139

Kudos [?]: 58 [0], given: 90

Location: India
WE: Engineering (Energy and Utilities)
Re: What is the greatest value of y such that 2^y is a factor of 11! ? [#permalink]

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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

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

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

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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

Intern
Joined: 18 May 2016
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Kudos [?]: 1 [0], given: 7

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

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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

Target Test Prep Representative
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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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12 Dec 2016, 18:14
1
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Expert's post
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!.

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Jeffery Miller

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

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