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find the maximum power of 6 that wil divide 65 18 Aug 2006, 14:34
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find the maximum power of 6 that wil divide 65!



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find the maximum power of 6 that wil divide 65 18 Aug 2006, 14:38
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Is it 10 by any chance....
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find the maximum power of 6 that wil divide 65 Updated on: 19 Aug 2006, 08:38
Originally posted by haas_mba07 on 18 Aug 2006, 14:48.
Last edited by haas_mba07 on 19 Aug 2006, 08:38, edited 1 time in total.
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Never mind... didn't get the question at all... :oops:
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find the maximum power of 6 that wil divide 65 18 Aug 2006, 15:08
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The crux of the issue is: if we found the prime factorization of 65!, what would be the power of 3?
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find the maximum power of 6 that wil divide 65 18 Aug 2006, 15:29
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kevincan
The crux of the issue is: if we found the prime factorization of 65!, what would be the power of 3?
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Thanks ! That is a great tip indeed... so the answer should be 13...

I tried combining groups of (2*3) but obviously did not realize that there are enough 2's... for all the 3's
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find the maximum power of 6 that wil divide 65 18 Aug 2006, 17:33
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fresinha12
find the maximum power of 6 that wil divide 65!
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6= 3*2

# of factors of 3 in 65 = 21
# of factors of 3 with two 3's = 9 18 27 36 45 54 63= 7
# of factors of 3 with three 3's = 27 54 = 2

# of factors of 2 in 65 where 2 appears once= 32

Total # of 3's = 21+7+2=30

Hence 6^30 ??

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find the maximum power of 6 that wil divide 65 18 Aug 2006, 17:42
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kevincan
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The crux of the issue is: if we found the prime factorization of 65!, what would be the power of 3?

Thanks ! That is a great tip indeed... so the answer should be 13...

I tried combining groups of (2*3) but obviously did not realize that there are enough 2's... for all the 3's

???
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Oops.. I think my mind is not functioning... I got 30 finally..
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find the maximum power of 6 that wil divide 65 18 Aug 2006, 21:56
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30

terms divisible by 3 = 21
terms divisible by 9 = 7
terms divisible by 27 = 2

Total = 21+7+2 = 30



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