GCFs+and+LCMs

Least Common Multiple Greatest Common Factor The **greatest common factor **, or **GCF **, is the **greatest factor ** that divides two numbers. To find the **GCF ** of two numbers: List the prime **factors ** of each number. Multiply those **factors ** both numbers have in **common **. If there are no **common **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">prime **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">factors **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">, the **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">GCF **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> is 1.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">Factors are numbers you can multiply together to get another number:

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">Example: 2 and 3 are factors of 6, because 2 × 3 = 6.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">A number can have MANY factors!

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">Example: What are the factors of 12?

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">3 and 4 are factors of 12, because 3 × 4 = 12.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">Also 2 × 6 = 12 so 2 and 6 are also factors of 12.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">So 1, 2, 3, 4, 6 and 12 are all factors of 12

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives makes a positive. =**F-Chart Factoring:**=

=**T-Chart Factoring:**=

=**Birthday Cake Factors:**=


 * How many layers is this cake for a one year old?**

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 * Prime and Composite**



Factor Trees:

Deciduous:







Prime Factorization Video

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=**Factor Rainbows:**=



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media type="custom" key="28672546" <span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">In Algebra, factors are what you can multiply together to get an expression.

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">(x+3) and (x+1) are factors of x <span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif;">2 <span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;"> + 4x + 3:

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">What is prime factorization?

<span style="background-color: #eeeeff; color: #000088; font-family: Verdana,Georgia,serif; font-size: 16px;">Here is a link to a video:

ICoachMath.com

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=**Factor Pairs:**=

= = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">The **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">greatest common factor **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">, or **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">GCF **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">, is the **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">greatest factor **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> that divides two numbers. To find the **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">GCF **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> of two numbers: List the prime **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">factors **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> of each number. Multiply those **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">factors **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> both numbers have in **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">common **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">. If there are no **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">common **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> prime **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">factors **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">, the **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;">GCF **<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 16px;"> is 1.



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media type="youtube" key="jFd-6EPfnec" width="420" height="315" Upside Down Birthday Cake:

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=**Multiples:**=



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=**Multiples and Factors Venn Diagram:**=









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