Tuesday 2/12

Hello all. Just a quick note about showing work - please remember to show your work by hand. While a few of you got all of the answers correct for the blog questions from Friday, I didn't see any of your work, and was not able to tell if you found those answers by using the prime factorization method or the listing method.

Right now, it's important that you're using the prime factorization method specifically so that we can move on to the next step.

If you finished your work Friday, it will be passed back to you with comments I've made. If not, please take it out. Everyone should compare their work from Friday to the answers on today's blog. Let's take a look at how we can find the GCF of each set of numbers by using the prime factorization method:

1)  16, 60

First, find the prime factorization of each:

Next, identify the matches on each side. A "match" is when there's a number on one side (at the bottom of the tree) that has an EXACT twin on the other side. The two numbers team up to create a "match."

We have underlined our matches. There's a "2" on one side, and another "2" on the other side. This gives us our first match: 2. Our second match is also 2, since there is a second two on both sides. As shown in the picture below, the remaining numbers have no matches:

Now, list our matches. We have one match of "2" and another match of "2". We multiply our matches together:

The GCF = 4.


Let's look @ #2 from yesterday's blog:

2)  36, 81

Step 1: Find the prime factorization of both numbers. Then, find your matches:

The 1st 3 on the left side matches with the 1st 3 on the right side. This gives us our first match of "3." The next 3 on the left side matches with the second 3 on the right side. This gives us another match of "3." None of the other numbers have matches. So, our matches are 3 and 3. Now, we multiply our matches to get a GCF of 9:

3)  15, 30

Here's one big diagram that puts everything together (click the pic to make it bigger):

4)  32, 64

We had five 2s on the left side, which all had matches on the right side. So our matches are 2, 2, 2, 2, and 2:

5)  10, 13 --- Don't forget that every number has a factor of "1":

That was a tricky one :). Now we need more practice. Your classwork today will be collected. Please hand in Friday's work as well if you have not already done so. I will be checking for work shown - this is the most important part, so I can help you when you make a mistake.
Let's try the following five problems. Same directions as Friday - find the GCF of each pair of numbers using the prime factorization method. 

1)   18, 24
2)   36, 54
3)   75, 100
4)   24, 36
5)   30, 90