Factor Expressions using GCF

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Question 1 of 4

1. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $54$ $54$ , $63$ $63$ , and $180$ $180$
- (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 $54$ $54$ :

Factors of $63$ $63$ :

Factors of $180$ $180$ :

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

Factors of $54$ $54$ :

Factors of $63$ $63$ :

Factors of $180$ $180$ :

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

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

$=$ $=$ $9$ $9$

$9$ $9$
Question 2 of 4

2. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $12 m^{2} n$ $12m^2n$ and $90 m^{2} n^{2} p$ $90m^2n^2p$
- 1. $3 m n^{2}$ $3mn^2$
- 2. $3 m n$ $3mn$
- 3. $6 n^{2}$ $6n^2$
- 4. $6 m^{2} n$ $6m^2n$
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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 $12 m^{2} n$ $12m^2n$ :

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

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

Factors of $12 m^{2} n$ $12m^2n$ :

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

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

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

$=$ $=$ $6 m^{2} n$ $6m^2n$

$6 m^{2} n$ $6m^2n$
Question 3 of 4

3. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $18 a^{2}$ $18a^2$ , $30 a b$ $30ab$ , and $54 b$ $54b$
- (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 $18 a^{2}$ $18a^2$ :

Factors of $30 a b$ $30ab$ :

Factors of $54 b$ $54b$ :

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

Factors of $18 a^{2}$ $18a^2$ :

Factors of $30 a b$ $30ab$ :

Factors of $54 b$ $54b$ :

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

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

$=$ $=$ $6$ $6$

$6$ $6$
Question 4 of 4

4. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $32 x^{2} y$ $32x^2y$ , $96 x^{2} y^{3}$ $96x^2y^3$ , and $128 x^{2} y^{2}$ $128x^2y^2$
- 1. $32 x^{2} y$ $32x^2y$
- 2. $12 x^{2}$ $12x^2$
- 3. $16 x y$ $16xy$
- 4. $8 x y^{2}$ $8xy^2$
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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 $32 x^{2} y$ $32x^2y$ :

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

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

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

Factors of $32 x^{2} y$ $32x^2y$ :

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

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

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

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

$=$ $=$ $32 x^{2} y$ $32x^2y$

$32 x^{2} y$ $32x^2y$

Factor Expressions using GCF

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

GCF	$=$ $=$	$3$ $3$ $\times$ $times$ $3$ $3$
	$=$ $=$	$9$ $9$

GCF	$=$ $=$	$3$ $3$ $\times$ $times$ $2$ $2$ $\times$ $times$ $m$ $m$ $\times$ $times$ $m$ $m$ $\times$ $times$ $n$ $n$
	$=$ $=$	$6 m^{2} n$ $6m^2n$

GCF	$=$ $=$	$3$ $3$ $\times$ $times$ $2$ $2$
	$=$ $=$	$6$ $6$

GCF	$=$ $=$	$2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $x$ $x$ $\times$ $times$ $x$ $x$ $\times$ $times$ $y$ $y$
	$=$ $=$	$32 x^{2} y$ $32x^2y$