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If x is an integer, what is the largest value of x such that 2^x is a

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Bunuel
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If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  15 Apr 2016, 01:28
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If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800
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Abhishek009
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  15 Apr 2016, 11:37
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Bunuel wrote:
If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800


\(72^{20}\) = \((8 * 9)^{20}\)

=> \((2^3*3^2)^{20}\)

=> \((2^{60}*3^{40})\)

For \(2^x\) to be a factor of \((2^{60}*3^{40})\) the minimum value of x must be 60

Answer should be (C) :-D 8-)
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  15 Apr 2016, 03:40
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If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800

IMO C is the answer.
72/2 + 72/4 +72/16 + 72/32 + 72/64
36 + 18 + 4 + 2 + 1 = 61
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  16 Apr 2016, 00:35
2^x is a divisor of 72^20 so,

72^20 / 2^x = k (with k an integer)
(9*8)^20 / 2^x = k
(3^40)(2^60) / 2^x = k

max value of x for k to be an integer is x=60 since 3^40 will yield any power of 2...

answer C
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stonecold
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  03 May 2016, 08:19
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Please Update the answer..!!
Frustrating watching the right bulb flash :(

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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  03 May 2016, 08:38
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Bunuel wrote:
If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800


Hi,
pl update the OA..
It is erroneously marked D whereas it should be C
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Bunuel
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  03 May 2016, 09:30
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chetan2u wrote:
Bunuel wrote:
If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800


Hi,
pl update the OA..
It is erroneously marked D whereas it should be C

__________
Done. Thank you.
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ScottTargetTestPrep
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  12 Dec 2019, 19:53
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Bunuel wrote:
If x is an integer, what is the largest value of x such that 2^x is a factor of 72^20?

A. 0
B. 20
C. 60
D. 160
E. 1,800


Breaking 72^20 into primes, we have:

72^20 = (2^3 x 3^2)^20 = 2^60 x 3^40

Answer: C
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Re: If x is an integer, what is the largest value of x such that 2^x is a [#permalink] New post  07 Dec 2023, 07:44
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