Prime factorization!
Those two words have always caused me some anxiety and a bit of nail biting. So, when I saw that we were covering this
topic in my Math for Elementary Teachers class, I was a little nervous. After all, it has been quite a
while since I really looked at factoring numbers. However, I am happy to say that I made it
through with my nails still intact and a much better understanding of prime
factorization.
What’s so bad about
prime factorization?I had to ask myself this question as I started looking at prime factorization again. Why all the anxiety over a few little numbers? At some point in my past I must have had a bad experience with prime numbers. Or, maybe it is just the word, “factorization”, that seems so daunting to me. Either way, I found out that it is not as complicated as it sounds! As a matter of fact, I almost would go so far as to say…I actually enjoyed it.
How does it work?
Prime factorization is basically breaking a number down to
its prime factors. A prime number is one
that only has two factors, 1 and itself.
For example, the number 7 only has factors of 1 and 7. No other numbers can be multiplied together
to make 7. So, 7 is a prime number. The
first five prime numbers are 2, 3, 5, 7 and 11.
If I am going to find the prime factorization of the number
84, I start by dividing it by the lowest prime number that can go into it. If I am not sure of what the lowest prime is
that can go into 84, then I can use the rules of divisibility
to help me find it. I know that 84 can
be divided by 2 and that 2x42=84. Now I move on to find the lowest prime number
that can go into 42. This would be 2 again and 2x21=42. Now I need to find the lowest prime number
that goes into 21. This would be 3 and 3x7=21. Since 3 and 7
are both prime numbers, I can divide no further. I end up with the prime factorization for 84
being 2x2x3x7. Here is a video which
shows how to use a factor
tree to find the prime factorization
of 84.
Here is a math manipulative that can be used to practice
making factor trees and finding the prime factorization of numbers:
Factor Tree Manipulative
Why is prime
factorization necessary?
Prime factorization is a great resource to use when we need
to find the greatest common factor (GCF) or least common multiple (LCM) of two
numbers. It works especially well if we
need to find these things when we are working with large numbers. Sounds like a topic for another post! Here
are a couple of links to show how we find the GCF and LCM with prime
factorization: Using prime factorization to find the LCM
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