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If k is a positive integer and 269!/2^k is a positive integer, what is

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Bunuel
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If k is a positive integer and 269!/2^k is a positive integer, what is [#permalink] If k is a positive integer and 269!/2^k is a positive integer, what is   21 Mar 2023, 01:30
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If k is a positive integer and \(\frac{269!}{2^k}\) is a positive integer, what is the greatest possible value of k ?

A. 262
B. 263
C. 264
D. 265
E. 266



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D
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Re: If k is a positive integer and 269!/2^k is a positive integer, what is [#permalink] If k is a positive integer and 269!/2^k is a positive integer, what is   21 Mar 2023, 01:55
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We need to find the number of 2's in 269!.
An elegant method to solve such problem is -
269/2 = 134 (ignore remainder 1)
134/2 = 67
67/2 = 33 (ignore remainder 1)
33/2 = 16 (ignore remainder 1)
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1
Now find 134 + 67 + 33 + 16 + 8 + 4 + 2 +1 = 265
Answer D
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Re: If k is a positive integer and 269!/2^k is a positive integer, what is [#permalink] If k is a positive integer and 269!/2^k is a positive integer, what is   11 May 2024, 04:20
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Re: If k is a positive integer and 269!/2^k is a positive integer, what is [#permalink]
11 May 2024, 04:20
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