What is the prime factorization of a number used for?

Answer 1

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 government. 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.