Factor Expressions using GCF

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Question 1 of 4

1. Question
Find the greatest common factor ( $GCF$ ) of $54$ , $63$ , and $180$
- (9)
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A Greatest Common Factor is the factor of two terms with the highest value.

Draw a factor tree for both terms and find their common factors

Factors of $54$ :

Factors of $63$ :

Factors of $180$ :

Next, highlight the common factors that both terms have and find the one with the highest value.

Factors of $54$ :

Factors of $63$ :

Factors of $180$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $3$ $times$ $3$

$=$ $9$

$9$
Question 2 of 4

2. Question
Find the greatest common factor ( $GCF$ ) of $12m^2n$ and $90m^2n^2p$
- 1. $6m^2n$
- 2. $3mn$
- 3. $6n^2$
- 4. $3mn^2$
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A Greatest Common Factor is the factor of two terms with the highest value.

Draw a factor tree for both terms and find their common factors

Factors of $12m^2n$ :

Factors of $90m^2n^2p$ :

Next, highlight the common factors that both terms have and find the one with the highest value.

Factors of $12m^2n$ :

Factors of $90m^2n^2p$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $3$ $times$ $2$ $times$ $m$ $times$ $m$ $times$ $n$

$=$ $6m^2n$

$6m^2n$
Question 3 of 4

3. Question
Find the greatest common factor ( $GCF$ ) of $18a^2$ , $30ab$ , and $54b$
- (6)
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A Greatest Common Factor is the factor of two terms with the greatest value.

Draw a factor tree for both terms and find their common factors

Factors of $18a^2$ :

Factors of $30ab$ :

Factors of $54b$ :

Next, highlight the common factors that both terms have and find the one with the highest value.

Factors of $18a^2$ :

Factors of $30ab$ :

Factors of $54b$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $3$ $times$ $2$

$=$ $6$

$6$
Question 4 of 4

4. Question
Find the greatest common factor ( $GCF$ ) of $32x^2y$ , $96x^2y^3$ , and $128x^2y^2$
- 1. $32x^2y$
- 2. $16xy$
- 3. $12x^2$
- 4. $8xy^2$
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A Greatest Common Factor is the factor of two terms with the highest value.

Draw a factor tree for both terms and find their common factors

Factors of $32x^2y$ :

Factors of $96x^2y^3$ :

Factors of $128x^2y^2$ :

Next, highlight the common factors that both terms have and find the one with the highest value.

Factors of $32x^2y$ :

Factors of $96x^2y^3$ :

Factors of $128x^2y^2$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $2$ $times$ $2$ $times$ $2$ $times$ $2$ $times$ $2$ $times$ $x$ $times$ $x$ $times$ $y$

$=$ $32x^2y$

$32x^2y$

Factor Expressions using GCF

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1. Question

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Exceptional!

2. Question

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Correct!

3. Question

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Great Work!

4. Question

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Fantastic!

Quizzes

GCF	$=$	$3$ $times$ $2$ $times$ $m$ $times$ $m$ $times$ $n$
	$=$	$6m^2n$

GCF	$=$	$2$ $times$ $2$ $times$ $2$ $times$ $2$ $times$ $2$ $times$ $x$ $times$ $x$ $times$ $y$
	$=$	$32x^2y$