Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

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Algebra 1

Find the Greatest Common Factor: Mini-Lesson Review

Algebra 1Find the Greatest Common Factor: Mini-Lesson Review

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Mini Lesson Question

Which is the greatest common factor of

48

and

80

$40$
$24$
$8$
$16$

Find the Greatest Common Factor

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 $36$ .

A factor tree for 54: 54 splits into 9 and 6. 9 splits into 3 and 3. 6 splits into 2 and 3. The prime factors 3, 3, 3, and 2 are highlighted in boxes.

A factor tree for 36. 35 splits into 6 and 6. 6 splits into 2 and 3. 6 splits into 2 and 3. The prime factors 3, 2, 3, and 2 are highlighted in boxes.

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 $18$ .

Try it

Try It: Find the Greatest Common Factor

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 $56$ .

A factor tree for 84: 84 splits into 14 and 6. 14 splits into 2 and 7. 6 splits into 2 and 3. The prime factors 2, 7, 2, and 3 are highlighted in boxes.

A factor tree for 56: 56 splits into 4 and 14. 4 splits into 2 and 2. 14 splits into 2 and 7. The prime factors 2, 2, 2, and 7 are highlighted in boxes.

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

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

Factorizations of 84 and 56 are shown, with 84 = 2 times 2 times 3 times 7 and 56 = 2 times 2 times 2 times 7; matching factors are circled to highlight common factors between the two 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 $28$ .

Check Your Understanding

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

Multiple Choice:

$24$
$12$
$36$
$48$

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

Videos: Greatest Common Factor of Two Integers

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

Khan Academy: Greatest common factor explained

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/6-find-the-greatest-common-factor-mini-lesson-review

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.