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### Course: 6th grade (Illustrative Mathematics) > Unit 7

Lesson 16: Lesson 16: Common factors# Greatest common factor review

Review greatest common factors (GCF) and try some practice problems.

## What is GCF?

**GCF**stands for greatest common factor. The greatest common factor of two numbers is the greatest number that is a factor of both of them.

## Finding greatest common factor

One way to find the GCF of two (or more!) numbers is to list the factors of each number and find the greatest factor they have in common.

*Want to learn more about greatest common factors? Check out this video.*

### Example: GCF of $12$ and $18$

Factors of $12$ : ${1},{2},{3},4,{6},12$

Factors of $18$ : ${1},{2},{3},{6},9,18$

## Want to join the conversation?

- are factor and divisor the same thing?(28 votes)
- factors are for multiplication.

divisors are for division.(14 votes)

- some body said to use the Euclidean Algorithm, but I have no idea what that is :gcd( 118, 204 )

= gcd ( 118, 204 - 118 )

= gcd ( 118, 86 )

= gcd ( 118 - 86, 86 )

= gcd ( 32, 86 )

= gcd ( 32, 86 - 32 )

= gcd ( 32, 54 )

= gcd ( 32, 54 - 32 )

= gcd ( 32, 22 )

= gcd ( 10, 22 )

= gcd ( 10, 2 )

= 2

-Like whaaaaaaaat? I just you my brain so can some body please tell me: WHAT IS THIS?(14 votes)- Don't use the Euclidean Algorithm because while it does work, it is inefficient and mistakes will most likely happen around the middle. Try using prime factorization instead. it is much faster than using the Euclidean Algorithm.(4 votes)

- What is a quicker way to do this?(10 votes)
- A very quick way is to use the cake/ladder method.(9 votes)

- this is comfusing can you help(10 votes)
- so just list all its divisors and see the biggest one that divides both of them.(2 votes)

- as my fortune cookie once said "never let things that dont matter distract you" :)(10 votes)
- I'm a little bit confused but I'm confident that my scores going to be good Hope me luck (<0>_<0>)(6 votes)
- why wold we do this(6 votes)
- that was super easy(5 votes)
- pretty simple for math.(4 votes)
- where do i find more gcf practice(2 votes)
- Or maybe try IXL.COM(5 votes)