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## 6th grade (Illustrative Mathematics)

### Unit 7: Lesson 16

Lesson 16: Common factors# Greatest common factor review

CCSS.Math:

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: start color #11accd, 1, end color #11accd, comma, start color #11accd, 2, end color #11accd, comma, start color #11accd, 3, end color #11accd, comma, 4, comma, start color #11accd, 6, end color #11accd, comma, 12

Factors of 18: start color #11accd, 1, end color #11accd, comma, start color #11accd, 2, end color #11accd, comma, start color #11accd, 3, end color #11accd, comma, start color #11accd, 6, end color #11accd, comma, 9, comma, 18

start color #11accd, 1, comma, 2, comma, 3, end color #11accd and start color #11accd, 6, end color #11accd are common factors of 12 and 18. Which of these is the greatest?

start color #11accd, 6, end color #11accd is the greatest factor that 12 and 18 have in common.

## Want to join the conversation?

- are factor and divisor the same thing?(16 votes)
- factors are for multiplication.

divisors are for division.(3 votes)

- this is comfusing can you help(8 votes)
- so just list all its divisors and see the biggest one that divides both of them.(0 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?(7 votes)- This is just a fast way to find the GCF if you understand it.(1 vote)

- Because u don't want to do it.(13 votes)

- How do i not know this?! 😰(4 votes)
- Because you do not know(3 votes)

- this is so hard(4 votes)
- what is the difference between a factor and a denominator?(0 votes)
- The difference is that a factor is a number that goes with another number that can multiply and make it. A denominator is the bottom number of a fraction. It divides the numerator which is the top.(8 votes)

- How Do You do this I am so confused on it I only got 3 out of 7 right(5 votes)
- Same I get the same anwser as you(1 vote)

- how we going to do if it's really hard hint or video(3 votes)
- where do i find more gcf practice(2 votes)
- Or maybe try IXL.COM(4 votes)