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## 6th grade (Eureka Math/EngageNY)

### Course: 6th grade (Eureka Math/EngageNY) > Unit 2

Lesson 4: Topic D: Number theory—thinking logically about multiplicative arithmetic- Divisibility tests for 2, 3, 4, 5, 6, 9, 10
- Recognizing divisibility
- The why of the 3 divisibility rule
- The why of the 9 divisibility rule
- Divisibility tests
- Intro to even and odd numbers
- Greatest common factor examples
- Greatest common factor explained
- Greatest common factor
- Greatest common factor review
- Least common multiple
- Least common multiple: repeating factors
- Least common multiple of three numbers
- Least common multiple
- Least common multiple review
- GCF & LCM word problems
- GCF & LCM word problems

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# 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?(19 votes)
- factors are for multiplication.

divisors are for division.(6 votes)

- What is a quicker way to do this?(8 votes)
- A very quick way is to use the cake/ladder method.(8 votes)

- this is comfusing can you help(9 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?(8 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.(2 votes)

- Because u don't want to do it.(17 votes)

- How do i not know this?! 😰(4 votes)
- where do i find more gcf practice(2 votes)
- Or maybe try IXL.COM(5 votes)

- this is so hard(4 votes)
- Try using the cake method, it is a fast and easy way to find the GCF. You can search it up online.(1 vote)

- 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)
- try prime factorization.(1 vote)