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What is the greatest integer x for which 24,300,000,000/2^x

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What is the greatest integer x for which 24,300,000,000/2^x  [#permalink]

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New post 13 Oct 2012, 08:18
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What is the greatest integer x for which 24,300,000,000/2^x is an integer?

A. 8
B. 9
C. 10
D. 11
E. 12

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Because 243 is odd (and actually is 3^5), this number can be rewritten as 243 * 10^8 - and because 243 is not divisible by 2, all of the 2s will come from 108. 108 = 28 * 58, and 58 (much like 35) will not produce any factors of 2 of its own. So this number is divisible by 28, making 8 the greatest possible value of x.

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Re: What is the greatest integer x for which 24,300,000,000 / 2x  [#permalink]

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New post 13 Oct 2012, 08:24
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thevenus wrote:
What is the greatest integer x for which 24,300,000,000 / 2x is an integer?

A.8
B.9
C.10
D.11
E.12


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Spoiler: :: OE
Because 243 is odd (and actually is 35), this number can be rewritten as 243 * 108 - and because 243 is not divisible by 2, all of the 2s will come from 108. 108 = 28 * 58, and 58 (much like 35) will not produce any factors of 2 of its own. So this number is divisible by 28, making 8 the greatest possible value of x.


The question should read:

What is the greatest integer x for which 24,300,000,000 / 2^x is an integer?

A. 8
B. 9
C. 10
D. 11
E. 12

\(\frac{24,300,000,000}{2^x}=\frac{243*10^8}{2^x}=\frac{243*5^8*2^8}{2^x}\). As we can see the greatest value of x is 8.

Answer: A.
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Re: What is the greatest integer x for which 24,300,000,000 / 2x  [#permalink]

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New post 24 Dec 2013, 04:31
you need to re-write this question before its on the random questions of the day, if its not correct.
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Re: What is the greatest integer x for which 24,300,000,000 / 2x  [#permalink]

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New post 24 Dec 2013, 05:19
If this is the question of the day then how come you guys made an error like this???
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Re: What is the greatest integer x for which 24,300,000,000/2^x  [#permalink]

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New post 24 Dec 2013, 06:50
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Re: What is the greatest integer x for which 24,300,000,000/2^x  [#permalink]

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New post 26 Feb 2014, 19:16
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243 is not divisible by 2, so just count the zero's in the number (which is 8)

So, Answer = 8 = A
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Re: What is the greatest integer x for which 24,300,000,000/2^x  [#permalink]

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New post 09 Jun 2017, 22:20
24300000000 = 243*10^8 = 243*(2^8*5^8)
Hence greatest power of 2 is 8.
Answer A.
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Re: What is the greatest integer x for which 24,300,000,000/2^x  [#permalink]

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New post 11 Apr 2019, 11:43
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Re: What is the greatest integer x for which 24,300,000,000/2^x   [#permalink] 11 Apr 2019, 11:43
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