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### Unit 6: Lesson 11

Greatest common factor

# 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$12 and $18$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.
start text, g, c, f, end text, left parenthesis, 12, comma, 18, right parenthesis, equals, 6

## Practice

Problem 1
What is the greatest common factor of 8 and 14?
Another way to say this is:
start text, g, c, f, end text, left parenthesis, 8, comma, 14, right parenthesis, equals, question mark

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• are factor and divisor the same thing?
• factors are for multiplication.
divisors are for division.
• What is a quicker way to do this?
• A very quick way is to use the cake/ladder method.
• this is comfusing can you help
• so just list all its divisors and see the biggest one that divides both of them.
• 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?
• 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.
(1 vote)
• why do i hate math
• Because u don't want to do it.
• How do i not know this?! 😰
• Because you do not know
• this is so hard