1. Greatest Common Factor
Find it using a Venn Diagram

2. Greatest Common Factor
Sometimes, it is very easy to find the Greatest Common Factor of 2 numbers. For example, what is the Greatest Common Factor of 15 and 10?
5 
Greatest Common Factor

3. Greatest Common Factor
Most of the time, however, it is a little more difficult, and so today we are going to take some notes together on a great method to find the Greatest Common Factor of 2 numbers.
Sooooooo, please take out a blank sheet of paper, and get ready to take some notes.
Greatest Common Factor

4. Finding the Greatest Common Factor – Step 1.
Example: Find the GCF of 54 and 36
STEP 1: Use a factor tree to find the prime factorization of both numbers.
2 2
Finding the Greatest Common Factor – Step 1.

5. Finding the Greatest Common Factor – Step 1.
The prime factorization of 54 is:
2 x 3 x 3 x 3
The prime factorization of 36 is:
3 x 3 x 2 x 2
Finding the Greatest Common Factor – Step 1.

6. Finding the Greatest Common Factor – Step 2.
Step 2: Create a Venn Diagram (2 overlapping circles). For each pair of common prime factors, put one of those in the middle.
Finding the Greatest Common Factor – Step 2.

7. Finding the Greatest Common Factor – Step 2.
Example: 3 2
Finding the Greatest Common Factor – Step 2.

8. Finding the Greatest Common Factor – Step 3.
Step 3: Once you have put all of the pairs in the middle, multiply them together.
So, we need to multiply 3 x 3 x 2
The Greatest Common Factor of 54 and 36 is 18
Finding the Greatest Common Factor – Step 3.