What we learned in Ms Pahlevanlu’s math 10 classe this week…Some of what I learned this week was review, but a lot was relearning how to do the simple things like finding the GCF and the LCM (and long division 🙂 ), so learning these methods was really helpful to me.

When trying to find the GCF or the LCM, the methods are very similar until the last couple steps. For both the GFC and the LCM, you have to use prime factorization, which is basically using long division to find all of the undivisable factors, or the prime factors. When using prime factorization, you either use a tree diagram or a division table and you just divise out all the factors until you get only prime factors. After this, the GCF and the LCM begin to differ slightly in their method’s. For the GCF, you go through all the prime factors of the 2 or more numbers that you’re comparing, and you pull out all the prime factors that appear in all of the beginning numbers. With these factors you compare them and take the lowest possible exponent to go with the factor. Say if 25 and 40 both have fives as a prime factor, but in the 25 factorization, the five has a 2 as an exponent and in the 40 factorization, ere is only one five, you take the one. Then you multiply all the picked out factors and voila, you have you GCF.

For the LCM, you do prime factorization like I said, and then you write down all the prime factors, instead of just the ones that appear in all the numbers. Then you compare the factors, and take the highest possible exponent. Instead of the five with a one for an exponent, you take the five with a two for an exponent, then you multiply all the numbers together, and voila again, you have you LCM.