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This was the question:

Why learn prime factorization? How does it apply to the real world?

Professor Homunculus' answer:

That's a good question. People are always asking things like "Why do we have to learn such-and such?" I wish ever teacher first explained the greater value of math in a person's life (like how to make informed, mature decisions) before they loaded you up with "information". Then we'd understand that math is more than a bunch of apparently random formulae. But first we have to get the teachers to understand this!

Let's say you don't intend to ever become a mathematician, so what would you need to know something like prime factorization for? Here's a roundabout, but a good, answer:

When you look behind the Idea of what prime factorization is, you will see that it is about breaking things down to their most basic parts. If you pay attention to the world, and your mind, when you learn math, you will get great life-lessons from learning about things like how we sort the world. Sorting numbers is great lesson in sorting reality.
What the hell do I mean by this?

OK, an example: let's say you are trying to understand the way a good government works. You decide, (or discover) what the basic, inalienable parts are. That means things which you can never, ever break if you want to build a good government. I would say the first 10 amendments of the Constitution of the United States (also known as "The Bill of Rights" are a good example. You cannot break those laws while making other laws, and still have a good goverment. They are the PRIME FACTORS in making laws.

A great example is the 8th Amendment, which states, "Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted." No one can make a just law that goes against that amendment (or any other) without it being "unconstitutional" (breaking the prime law - the Constitution - that which constitutes what the nation is based upon).

What does this really have to do with Prime Factors? If you understand the Bill of Rights, you can see that there is no way that cruel and unusual punishment will ever fit in with being a good American (or anyone else, either!) If you understand prime factorization you will see that there is no way that 4 is going to fit among the prime factors of 21. If you spend enough time and learn any concept of math well enough, it will help you understand how things in general work.

Math is about seeing how things fit it. It is the science of (among other things) patterns and order. If you learn to accept math as a way to describe and think about certain parts of reality, you will get "the big picture" - the picture of math as something beyond just a boring subject in school.


By the way, if some idiot gives you the "You-have-to-learn-it in-order-to-pass-the-test"-routine, be skeptical about there answers to other things, too. They have no Idea about math. They are robots. Smile, jump through their hoops, and be glad you don't have to spend much more time in your life with them. You may have to pass their tests, but please be assured that there is much greater value than silly tests in learning how your world works. Learn the drivel they teach you so you can spit it back at them and get the grades you want, but ask more mature people about the real reasons behind stuff. Remember, "Excellence is the best revenge!"

What did I learn from math in public school? I learned that most teachers are nice, but don't have a clue about teaching math, and that most of the administrators suck and don't have a clue about education in general. That's a more important lesson than the stuff they teach for the test.

Keep your eyes wide open, and enjoy the ride,

Professor Homunculus

If you this actually inspires you to learn something about prime factorization, you can learn it at The Pretty Good Guide to Prime Factorization .


Corrollary thought:

If you understand the difference between a factor and a prime factor, you can see the correlation to that and the difference between a local law and a constitutional law.

The basis of all other laws can be deduced from the Constitution . From the 8th Amendment, you can be sure that no other laws (ones which will stand, anyway) will be able to be made that will violate it. But you cannot deduce from any specific local law what the constitutional law is.

This is just like factors and prime factors. If you know that 4 is a factor of a number, then you can deduce that 2 will be a prime factor. But if you merely know that 2 is a prime factor of a number, you can’t be sure that 4 will be a prime factor of that number. Take the number 6 for example: 2 is a prime factor, but 4 isn’t a factor at all.
On the other hand, you cannot find a number of which 4 is a factor, and 2 is not a prime factor. Try it.

Thoughts like this (even though my description of it is pretty sketchy!) are the basis of understanding logic and decision-making in the real world. The more you can abstract knowledge from lots of field, the more you will understand the world around you.

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