Nerd Pride Radio

Why are Powers of 2 not divisible by 3? I'd think by chance it would be but the fact that it's never. Then I'd think that
there's obviously a rule about it, like "the dual power triforce dividing rule" or something, but I've seen no mention.

Is this interesting, or a DUH that my brain doesn't quite get.

https://docs.google.com/spreadsheets/d/ ... ingle=true

Well- I mean- as a "power of two" any of them can ultimately only break down to the prime numbers of 2. By your definition, they can't be broken down to a factor of three. I feel like you're setting up your definition to exclude a factor of three because every number is going to be 2x2 or 2x2x2 or 2x2x2x2 and so on.

Hmmm... I think I'm starting to get it.

Now seeing that any power of 2 is not divisible by 3,5,7,11,13, and I'm assuming any future odd/prime numbers.

And the basic that odd*odd = odd, and odd*even = even

And... I'm lost again. WAIT I think I'm getting it.

3, 9, 27, 81, no other primes divide with those
25, 125, same
49 same

Ok, so all powers of a prime number, when broke down to their smallest non-1 divisible components are all that prime number.

So Prime to the positive n power cannot is not divisible by any other prime number.

Whew. Ok.

That's numberwang!

Thanks Kyle