How to Find the Greatest Common Factor: 6 Steps (with Pictures) (2024)

Table of Contents

Comparing Common Factors Using Prime Numbers Community Q&A Video Tips You Might Also Like References About This Article Reader Success Stories Did this article help you? FAQs References

Download Article

Explore this Article

methods

1Comparing Common Factors

2Using Prime Numbers

Other Sections

Video

Tips and Warnings

References

Article Summary

Reviewed byGrace Imson, MA

Last Updated: March 25, 2024Fact Checked

Download Article

Finding the greatest common factor (GCF)^[1] of a number set can be easy, but there are several steps you'll need to follow to get there. In order to find the greatest common factor of two numbers, you'll need to factor out both of those numbers using your knowledge of timetables, then identify the largest number that appears in both sets of factors.

Method 1

Method 1 of 2:

Comparing Common Factors

Download Article

1
Find factors of the number. You don't have to know prime factorization to find the greatest common factor. Start by finding all the factors of the set you are comparing.^[2]
2
Compare the sets of factors until you find the biggest number that's in both sets.

Method 2

Method 2 of 2:

Using Prime Numbers

Download Article

1
Factor each number completely into its prime numbers.^[3] A prime number is number greater than 1 that has no factors but itself. Examples of prime numbers include 5, 17, 97, and 331, to name just a few.
2
Identify any common prime factors.^[4] Pick out any prime numbers between the set that are the same. There can be several common factors, one common factor, or none.
See Also
Use List Method to Find GCF What are LCM and GCF? How do I find them easily?What Is the Greatest Common Factor (GCF)? Definition, Examples 6.2: Greatest Common Factor and Factor by Grouping
3
Calculate: If there are no common factors then the greatest common factor is 1. If there's only one prime common factor, then that's your common factor. If there are multiple prime common factors, then multiply all the prime common factors together to get your greatest common factor^[5].
4
To demonstrate this method, study this example.

Community Q&A

Add New Question

Question
What level of questions should I make for a test? Should I make the test easy, medium or hard?
Community Answer
It depends upon your knowledge of your students. If you see that your students are very competitive and clever, you can make the test hard, so as to challenge their knowledge about the subject. If your students are beginners and have a lot to learn yet, making it easier will encourage them to keep learning more.
Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow
YesNo
Not Helpful 29Helpful 60
Question
What's the greatest common factor of 4x^3y, 8x^2y^3, xy^3z^5?
Donagan
Top Answerer
The three terms are: 4x³y, 8x²y³, and xy³z^5. First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. The lowest x exponent is 1. The lowest y exponent is also 1. There is no z in two of the terms (so z is not a common factor). That means the greatest common factor among the three terms is 1xy (or xy).
Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow
YesNo
Not Helpful 21Helpful 40
Question
What is the use of prime numbers in our lives?
Donagan
Top Answerer
The average person is never likely to use prime numbers. They do have certain applications within science and mathematics.
Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow
YesNo
Not Helpful 23Helpful 57

See more answers

Video

Tips

Did you know that the mathematician Euclid of the third century B.C.E. created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials?^[6]
Thanks
Helpful1Not Helpful0
A prime number is a number that can only be divided by one and itself.
Thanks
Helpful3Not Helpful0

Submit a Tip

All tip submissions are carefully reviewed before being published

Submit

Thanks for submitting a tip for review!

How toFind the Greatest Common Divisor of Two IntegersHow toDo Math Proofs

How toMultiply With Your HandsHow toUse the Google CalculatorHow toLearn MathHow toSubtractHow toDivide Fractions by a Whole NumberHow toDo Long DivisionHow toDo DivisionHow toDo Long MultiplicationHow toDo Double Digit MultiplicationHow toMultiplyHow to Cross Multiply FractionsHow toDivide by a Two‐Digit Number

References

About This Article

Reviewed by:

Grace Imson, MA

Math Teacher

This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 413,246 times.

134 votes - 70%

Co-authors: 31

Updated: March 25, 2024

Categories: Featured Articles | Multiplication and Division

Article SummaryX

To find the greatest common factor of two or more numbers, make a list of all of the factors of each number. For example, for the number 10, the factors are 1, 2, 5, and 10, and for the number 21, the factors are 1, 3, 7, and 21. Then, compare the list of factors to find the largest number that the two have in common. For 10 and 21, the greatest common factor is 1. To learn more, like how to use prime numbers to find the greatest common factor, keep reading!

Did this summary help you?

In other languages

Italian

Spanish

Russian

French

Chinese

Indonesian

Vietnamese

Dutch

Arabic

Hindi

Thai

Korean

Japanese

Print
Send fan mail to authors

Thanks to all authors for creating a page that has been read 413,246 times.

Reader Success Stories

Bill Nye
Sep 22, 2016
"It was good. Just looking at it first glance, I understood everything."

Did this article help you?

How to Find the Greatest Common Factor: 6 Steps (with Pictures) (2024)

FAQs

What is the Greatest Common Factor for 6? ›

The factors of 6 are 1, 2, 3, 6 and factors of 6 are 1, 2, 3, 6. Therefore, the Lowest Common Multiple (LCM) of 6 and 6 is 6 and Highest Common Factor (HCF) of 6 and 6 is 6.

Read The Full Story ›

How to get GCF in grade 5? ›

To find the GCF, list all prime factors that are common between the two numbers and multiply them together. To find the LCM, multiply the GCF by all the prime factors of both numbers that have not yet been used. What is the difference between least common multiple (LCM) and least common denominator (LCD)?

Find Out More ›

How to find GCF fast? ›

Here's how to find the GCF of a set of numbers using prime factorization:

List the prime factors of each number.
Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.
Multiply all the circled numbers. The result is the GCF.

Jul 9, 2021

View Details ›

What are the steps for factoring? ›

Factorization of Quadratic Equations

Learn: Factorisation. ...
Step 1: Consider the quadratic equation ax² + bx + c = 0.
Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b. ...
Step 3: Now, split the middle term using these two numbers, ...
Step 4: Take the common factors out and simplify.

More items...

See Details ›

How to find factors of 6? ›

If we divide the number 6 by any numbers other than 1, 2, 3 and 6, then it leaves the remainder. Hence, the factors of 6 are 1, 2, 3 and 6.

Keep Reading ›

How to find common factors quickly? ›

To find common factors of two numbers, first, list out all the factors of two numbers separately and then compare them. Now write the factors which are common to both the numbers. These factors are called common factors of given two numbers.

Show Me More ›

How is GCF calculated? ›

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

Learn More Now ›

How do you explain GCF? ›

The greatest common factor (GCF) is the largest whole number which is shared by given numbers. For example, common factors of 10 and 20 are 1, 2, 5 and 10, but the highest of those is 10; therefore, the greatest common factor of 10 and 20 is 10.

Show Me More ›

How do you pull out GCF? ›

Factoring out the greatest common factor (GCF)

To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.

Show Me More ›

How to solve GCF problems? ›

How to Solve Greatest Common Factor Word Problems

Step 1: Identify what numbers of which we will find the GCF.
Step 2: Use the slide method to determine the GCF of these numbers.
Step 3: Provide the GCF in the context of the problem.

Apr 13, 2021

Read The Full Story ›

What is GCF in math Grade 7? ›

The greatest common factor (GCF) of two numbers is the largest factor of both numbers. It is the product of the common prime factors between them.

What is the easiest way to find the highest common factor? ›

The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.

Explore More ›

How do you find the greatest common factor simplified? ›

Factorize the numbers and identify all common factors. To get the GCF multiply all common factors. You can use the greatest common factor to simplify fractions. A ratio is an expression that tells us the quotient of two numbers.

Know More ›