Highest Common Factor 1

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Year 10

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Highest Common Factor

Highest Common Factor 1

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Question 1 of 5

1. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $3 y$ $3y$ and $12 y$ $12y$
- (3y)
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A Greatest Common Factor is the factor of two terms with the highest value.

Find the factors of both terms.

Factors of $3 y$ $3y$ : $3$ $3$ $\times$ $times$ $y$ $y$

Factors of $12 y$ $12y$ : $3$ $3$ $\times 4 \times$ $times4times$ $y$ $y$

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

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

$=$ $=$ $3 y$ $3y$

$3 y$ $3y$
Question 2 of 5

2. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $6 a$ $6a$ and $4 a b$ $4ab$
- (2a)
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A Greatest Common Factor is the factor of two terms with the highest value.

Find the factors of both terms.

Factors of $6 a$ $6a$ : $2$ $2$ $\times 3 \times$ $times3times$ $a$ $a$

Factors of $4 a b$ $4ab$ : $2$ $2$ $\times 2 \times$ $times2times$ $a$ $a$ $\times b$ $timesb$

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

GCF $=$ $=$ $2$ $2$ $\times$ $times$ $a$ $a$

$=$ $=$ $2 a$ $2a$

$2 a$ $2a$
Question 3 of 5

3. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $16 m$ $16m$ and $12 m n$ $12mn$
- (4m)
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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 $16 m$ $16m$ :

Factors of $12 m n$ $12mn$ :

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

Factors of $16 m$ $16m$ :

Factors of $12 m n$ $12mn$ :

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

GCF $=$ $=$ $2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $m$ $m$

$=$ $=$ $4 m$ $4m$

$4 m$ $4m$
Question 4 of 5

4. Question
Find the greatest common factor ( $G C F$ $GCF$ ) of $a^{2} b$ $a^2b$ and $a b^{2} c$ $ab^2c$
- (ab)
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A Greatest Common Factor is the factor of two terms with the highest value.

Find the factors of both terms.

Factors of $a^2b$ : $a$ $timesatimes$ $b$

Factors of $ab^2c$ : $a$ $times$ $b$ $timesbtimesc$

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

GCF $=$ $a$ $times$ $b$

$=$ $ab$

$ab$
Question 5 of 5

5. Question
Find the greatest common factor ( $GCF$ ) of $9u$ and $12u^2$
- (3u)
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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 $9u$ :

Factors of $12u^2$ :

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

Factors of $9u$ :

Factors of $12u^2$ :

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

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

$=$ $3u$

$3u$

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Quiz summary

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1. Question

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Correct!

2. Question

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Fantastic!

3. Question

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Nice Job!

4. Question

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Well Done!

5. Question

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Nice Job!

Quizzes

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

GCF	$=$ $=$	$2$ $2$ $\times$ $times$ $a$ $a$
	$=$ $=$	$2 a$ $2a$

GCF	$=$ $=$	$2$ $2$ $\times$ $times$ $2$ $2$ $\times$ $times$ $m$ $m$
	$=$ $=$	$4 m$ $4m$