Prime Factorization, GCF and LCM

   I was relieved to know we were moving on to this topic in chapter five.  I didn't enjoy our first chapter, sets and shading etc.  I absolutely hated that chapter and it even showed on my test.  Therefore, I am thankful we have test corrections in our class.  I am not going to lie, I was surprised when I realized what we were going to be doing.  I haven't heard of prime numbers, GCF and LCM in a very very long time which means I haven't done it. 
  I am expecting to do much better on this upcoming test.  I feel that I know and understand the material much better than last unit.  I don't mind doing the factor trees and figuring out problems.  I hope to do much better on the true or false section on this test. 
  What I really like about this unit is that there is a choice of methods to use to figure out the GCF or LCM.  I mentioned above that I don't mind the factor trees, which is one of the theorem's to choose from.  I am not a fan of the set intersection method for finding GCF.  It it too time consuming and there is always the possibility of missing a factor.  It can also be difficult for someone who doesn't know all the factors of different numbers, I am one of those people. 
  Another theorem I consider using to find the GCF is the subtracting method.  This method is good to use especially when the numbers aren't too large.  To start out it'd look like this GCF (350-250,250) and one would continue that until there are two similar numbers in the parentheses.  There is another theorem that deals with long division.  I personally haven't done long division without a calculator since elementary school.  I don't really bother with this method which is why I'm glad there's a choice. 
   It's always important to know that GCF, with prime factorization, needs the lowest exponent with only COMMON numbers.  Where as LCM needs the highest exponent with ALL numbers. 
  The prime factor test is the main thing I struggle with in this unit.  I confuse some of the rules to determine whether or not a number is prime.  I know how to figure the square root in that first step, which is why it's important to know all the numbers up to 100.  I know I have to test primes up to the first number.  From there I just seem to get confused.  I will just have to practice more on that part of the unit.  This time around I am not worried about this test and seem pretty confident.  I just hope my mathophobia doesn't kick in once I receive the test.