Math Is Fun Forum

Sudokuluvr

Member

Registered: 2006-11-07

Posts: 10

Number powers

I got a way to find the powers of a number. It's a very simple process..and I don't usually talk like that. You pick a number...say 6000. You would do this.

                                                 6000
                                             1,000 x 6
                                       100 x 10 x 3 x 2
                                     50 x 2 x 5 x 2 x 3 x 2
                                 25 x 2 x 2 x 5 x 2 x 3 x 2
                               5 x 5 x 2 x 2 x 5 x 2 x 3 x 2
It's basicly just giving equivalent equations to the one above it. Just using the factors of a certain number below it, unless it's prime. So when all the numbers are prime, you could out that there are 3 5's, 4 2's, and 1 3. So it would be, 5 to the third power, 2 to the third power, and 7 to the first power. If you multiply those numbers, they will equal 6000. It's basicly a type of division.... Well, if anyone here likes this let me know..and please post other cool stuff on my forum

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I'm the chosen one...deal with it

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Number powers

Yep.  It's call unique factorization of primes:

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Number powers

Yes, prime factoring is very useful. Unfortunately, it starts to become less useful as numbers get bigger. Your 6000 is nice because it has many factors, but something like 58517, for example, is a lot harder to break down.

You could probably still break that one down with persistence, but it's a lot harder, and as numbers get bigger they get increasingly difficult to break down. Once they're so big that they've got around 100 digits, not even computers can break them down into prime factors, and in fact, it is that that helps to keep important passwords and things encrypted safely.

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Number powers

Yes, prime factoring is very useful. Unfortunately, it starts to become less useful as numbers get bigger. Your 6000 is nice because it has many factors, but something like 58517, for example, is a lot harder to break down.

Maybe this is the case when you are asked to actually find the product of prime factors.  But because you can state it in general, it is extremely useful for theoretical mathematics.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."