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If 2^z is a factor of 25!, which of the following could be the value

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If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 28 Apr 2016, 04:50
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A
B
C
D
E

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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 29 Apr 2016, 00:08
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Bunuel wrote:
If 2^z is a factor of 25!, which of the following could be the value of z?

I. 22
II. 23
III. 24

A. I ​ only
B. II only
C. I​ and II
D. I, II, and III
E. None


2^z is a factor of 25!, what values can z take.

Powers of 2 in 25! = [25/2] + [25/4] +[25/8] + [25/16] , where [x] is the integral part of x
Powers of 2 in 25! = 12 + 6 + 3 + 1 = 22

Hence the maximum value of 2^z in 25! = 2^22
Only Statement I satisfies

Correct Option: A
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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 28 Apr 2016, 13:08
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Bunuel wrote:
If 2^z is a factor of 25!, which of the following could be the value of z?

I. 22
II. 23
III. 24

A. I ​ only
B. II only
C. I​ and II
D. I, II, and III
E. None



25! contains all numbers from 1 to 25. To find the factor with the highest power of 2, we count the number of multiples of 2,4,8 and 16

Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22

A is the answer.
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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 29 Oct 2016, 10:09
(25/2)+(25/4)+(25/8)+(25/16) = 12+6+3+1 = 22

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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 29 Oct 2016, 10:39
Bunuel wrote:
If 2^z is a factor of 25!, which of the following could be the value of z?

I. 22
II. 23
III. 24

A. I ​ only
B. II only
C. I​ and II
D. I, II, and III
E. None


25/2 = 12
12/6 = 3
3/2 = 1

12+3+1 = 22

So, Answer will be (A) Only I

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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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New post 24 Jan 2017, 19:13
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1) To paraphrase the question we need to find the total number of prime factors 2 in 25!
2) We need to count all the multiples of 2, add an additional two for every multiple of 2 that is also a multiples of 4, add an additional two for everything multiple of 2 that is also a multiple of 4 and multiple of 8, and add an additional two for every multiple of 2 that is also a multiple of 4, 6, 8, and 24.
3) 25/2=12; 25/4=6; 25/8=3; 25/24=1; 12+6+3+1=22
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Re: If 2^z is a factor of 25!, which of the following could be the value  [#permalink]

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Re: If 2^z is a factor of 25!, which of the following could be the value   [#permalink] 11 Dec 2019, 00:00
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