Find the Greatest Common Factor: Mini-Lesson Review

Which is the greatest common factor of

48

and

80

?

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.

Find the greatest common factor of $54$ and $36$ .

Step 1 - Factor each number into primes.

Factor $54$ and $36$ .

Step 2 - List the factors. In each column, circle the common factors.

Circle the $2$ , $3$ , and $3$ that are shared by both numbers.

Step 3 - Bring down the common factors that all the expressions share.

Bring down the $2$ , $3$ , and $3$ .

GCF $= 2 \cdot 3 \cdot 3$

Step 4 - Multiply the factors.

Multiply the common factors $2$ , $3$ , and $3$ .

GCF $= 18$

The GCF of $54$ and $36$ is $18$ .

Find the greatest common factor (GCF) of $84$ and $56$ .

Here’s how to find the GCF.

Step 1 - Factor each number into primes.

Factor $84$ and $56$ .

Step 2 - List the factors. In each column, circle the common factors.

Circle the $2$ , $2$ , and $7$ that are shared by both numbers.

Step 3 - Bring down the common factors that all the expressions share.

Bring down the $2$ , $2$ , and $7$ .

GCF $= 227$

Step 4 - Multiply the factors.

Multiply the common factors $2$ , $2$ , and $7$ .

GCF $= 28$

The GCF of $84$ and $56$ is $28$ .

Which is the greatest common factor of $96$ and $72$ ?

24

Check yourself: The GCF is the product of the common factors, 2 2 3.

Watch the following video to learn more about finding the greatest common factor of two integers.

Khan Academy: Greatest common factor explained