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## MAP Recommended Practice

### Course: MAP Recommended Practice>Unit 35

Lesson 18: 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.

### Example: GCF of $12$‍  and $18$‍

Factors of $12$: $1,2,3,4,6,12$
Factors of $18$: $1,2,3,6,9,18$
$1,2,3$ and $6$ are common factors of $12$ and $18$. Which of these is the greatest?
$6$ is the greatest factor that $12$ and $18$ have in common.
$\text{gcf}\left(12,18\right)=6$

## Practice

Problem 1
What is the greatest common factor of $8$ and $14$?
Another way to say this is:
$\text{gcf}\left(8,14\right)=?$

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.
• 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.
• this is comfusing can you help
• so just list all its divisors and see the biggest one that divides both of them.
(1 vote)
• why do i hate math
• Because u don't want to do it.
• as my fortune cookie once said "never let things that dont matter distract you" :)