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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.
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What makes a factorization of a number a prime factorization?
When all the factors are prime numbers, that's a prime factorization.
What is a diagram that shows the prime factorization of a number?
a prime factorization tree
What is the prime factorization of 397?
397 is a prime number, therefore prime factorization of 397 = 397.
What is the prime factorization of the number 26?
The prime factorization of the number 26 is: 2 x 13
Prime factorization for the number 54?
Prime factorization of the number 54 is 2 x 33.
How do you write out the prime factorization of a prime number?
The prime number is the prime factorization. For example, the prime factorization of the prime number 3 is 3. Get it?
Is 53 prime factorization number?
53 is a prime number so there is no relevant prime factorization for it.
What number has 2x2x2x2x3 as its prime factorization?
The only number with that prime factorization has to be 48.
How do you know without dividing that 91 is not in the prime factorization of 75257?
91 cannot be in the prime factorization of any number because it is not a prime number itself.
Can a number greater than 100 have only 1 number in it's prime factorization?
Yes. Any prime number greater than 100 has only itself in its prime factorization. Examples: The prime factorization of 101 is 101. The prime factorization of 109 is 109. The prime factorization of 127 is 127. The prime factorization of 311 is 311. The prime factorization of 691 is 691.
What makes a factorization of a number a prime factorization?
When all the factors are prime numbers, that's a prime factorization.
What is the prime factorization of 421?
421 is a prime number so it does not have prime factorization.
What is the prime factor of 19?
19 is a prime number, so it has no prime factorization.
What is the prime factorization for eighty-nine?
Since 89 is a prime number, the prime factorization of the number is simply 89.
What is a prime factorization for a number is 3x3x3x5x7?
That's the prime factorization of 945.
Is 23 a prime factorization?
23 is a prime number and does not require factorization.
What is a diagram that shows the prime factorization of a number?
a prime factorization tree
