Greatest Common Factor

Find it using a Venn Diagram

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

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.

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.

54 36

9 6 12 3

3 3 3 2 4 3 2 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 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.

Example:

3

3

2

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