LESSON: Greatest Common Factors

READ: Find the Greatest Common Factor Using Factor Trees

Find the Greatest Common Factor of Two or More Numbers Using Factor Trees

You just learned how to find the GCF by making lists. We can also find the GCF by making a factor tree. Let’s look at an example.

Example

Find the GCF of 20 and 30.

First, we make a factor tree for each number.

$& \ \ \ 20 && \quad \ \ 30\\ & \ \ \big / \ \big\backslash && \quad \ \big / \ \ \big\backslash\\ & \ 4 \quad 5 && \quad 5 \ \quad 6\\ & \big / \ \big\backslash && \qquad \ \big / \ \big\backslash\\ & 2 \ \ 2 && \qquad 3 \ \ \ 2\\ & 2^2 \times 5 && 5 \times 3 \times 2$

Here is a tricky one because there is more than one common factor. We have both five and two as common factors.

When you have more than one common factor, we multiply the common factors to find the GCF.

2 $\times$ 5 $=$ 10

10 is the greatest common factor (GCF).