anonymous
  • anonymous
find a number n such that \(2^n\) is divisible by 10
Mathematics
chestercat
  • chestercat
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lgbasallote
  • lgbasallote
how about n = 10?
anonymous
  • anonymous
NO such no exist
anonymous
  • anonymous
n = 10 -> 2^n = 1024, which is not divisible by 10. it doesn't exist? prove it! :-D

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anonymous
  • anonymous
For any no to be divisible by 10 it must have a factor of 5 in its prime factorization 5 can never occur in 2^n hence no such no exist
lgbasallote
  • lgbasallote
if we look at the powers of 2... 2 4 8 16 32 64 ...obviously...2 does not have a power that will make it end in 0...so no such number does exist :))) i just guessed that 10 a while ago hehe
anonymous
  • anonymous
right
anonymous
  • anonymous
It doesn't exist. If you list the powers of 2, you will notice that they end with the following digits: 2, 4, 8, 6, and this will repeat forever in this order.

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