# Finding the Greatest Common Factor

```Greatest Common
Factor
Find it using a Venn Diagram

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

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

Example: Find the GCF of 54 and 36

STEP 1: Use a factor tree to find the
prime factorization of both numbers.
54
36
9
3
3
6
3
12
2
4
2
3
3
2
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.

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.

Example:
3
3
2
Finding the Greatest Common
Factor – Step 2.

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.
```