Math / Algebra

QuestionFind the greatest common factor (GCF) of the expressions: $54x^3$ , $63x$ , and $54yx$ .

Studdy Solution

STEP 1

What is this asking? We need to find the biggest expression that divides evenly into $54x^3$ , $63x$ , and $54yx$ . Watch out! Don't forget to consider both the numbers and the variables when finding the GCF!

STEP 2

1. Find the GCF of the coefficients.
2. Find the GCF of the variables.
3. Combine to find the GCF of the expressions.

STEP 3

Let's list out the factors of each coefficient: $54$ : 1, 2, 3, 6, 9, 18, 27, 54 $63$ : 1, 3, 7, 9, 21, 63 $54$ : 1, 2, 3, 6, 9, 18, 27, 54

STEP 4

Looking at the lists, the greatest common factor of 54, 63, and 54 is 9!

STEP 5

The variables in our expressions are $x^3$ , $x$ , and $yx$ .
Notice that all expressions have a factor of $x$ , and only $x$ .
So, our GCF for the variables will definitely include $x$ .

STEP 6

$x^3$ can be written as $x \cdot x \cdot x$ , and $x$ is just $x$ .
Since we're looking for the greatest COMMON factor, we take the smallest power of $x$ present in all terms, which is $x^1$ or just $x$ . $y$ isn't in all the terms, so it won't be in our GCF.

STEP 7

We found that the GCF of the coefficients is 9 and the GCF of the variables is x.
When we put these together, we get $9 \cdot x = 9x$ .

STEP 8

The greatest common factor of $54x^3$ , $63x$ , and $54yx$ is $9x$ .

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QuestionFind the greatest common factor (GCF) of the expressions: $54x^3$ , $63x$ , and $54yx$ .

Studdy Solution

STEP 1

What is this asking? We need to find the biggest expression that divides evenly into $54x^3$ , $63x$ , and $54yx$ . Watch out! Don't forget to consider both the numbers and the variables when finding the GCF!

STEP 2

1. Find the GCF of the coefficients.
2. Find the GCF of the variables.
3. Combine to find the GCF of the expressions.

STEP 3

Let's list out the factors of each coefficient: $54$ : 1, 2, 3, 6, 9, 18, 27, 54 $63$ : 1, 3, 7, 9, 21, 63 $54$ : 1, 2, 3, 6, 9, 18, 27, 54

STEP 4

Looking at the lists, the greatest common factor of 54, 63, and 54 is 9!

STEP 5

The variables in our expressions are $x^3$ , $x$ , and $yx$ .
Notice that all expressions have a factor of $x$ , and only $x$ .
So, our GCF for the variables will definitely include $x$ .

STEP 6

$x^3$ can be written as $x \cdot x \cdot x$ , and $x$ is just $x$ .
Since we're looking for the greatest COMMON factor, we take the smallest power of $x$ present in all terms, which is $x^1$ or just $x$ . $y$ isn't in all the terms, so it won't be in our GCF.

STEP 7

We found that the GCF of the coefficients is 9 and the GCF of the variables is x.
When we put these together, we get $9 \cdot x = 9x$ .

STEP 8

The greatest common factor of $54x^3$ , $63x$ , and $54yx$ is $9x$ .

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QuestionFind the greatest common factor (GCF) of the expressions: 54x354x^354x3, 63x63x63x, and 54yx54yx54yx.

Studdy Solution

STEP 1

What is this asking? We need to find the biggest expression that divides evenly into 54x354x^354x3, 63x63x63x, and 54yx54yx54yx. Watch out! Don't forget to consider both the numbers and the variables when finding the **GCF**!

STEP 2

1. Find the GCF of the coefficients.2. Find the GCF of the variables.3. Combine to find the GCF of the expressions.

STEP 3

Let's **list out** the factors of each coefficient: 545454: 1, 2, 3, 6, 9, 18, 27, 54 636363: 1, 3, 7, 9, 21, 63 545454: 1, 2, 3, 6, 9, 18, 27, 54

STEP 4

Looking at the lists, the **greatest common factor** of 54, 63, and 54 is **9**!

STEP 5

The variables in our expressions are x3x^3x3, xxx, and yxyxyx.Notice that *all* expressions have a factor of xxx, and *only* xxx.So, our **GCF** for the variables will *definitely* include xxx.

STEP 6

x3x^3x3 can be written as x⋅x⋅xx \cdot x \cdot xx⋅x⋅x, and xxx is just xxx.Since we're looking for the **greatest COMMON factor**, we take the smallest power of xxx present in all terms, which is x1x^1x1 or just xxx. yyy isn't in all the terms, so it won't be in our **GCF**.

STEP 7

We found that the **GCF** of the coefficients is **9** and the **GCF** of the variables is **x**.When we put these together, we get 9⋅x=9x9 \cdot x = 9x9⋅x=9x.

STEP 8

The greatest common factor of 54x354x^354x3, 63x63x63x, and 54yx54yx54yx is 9x9x9x.

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QuestionFind the greatest common factor (GCF) of the expressions: $54x^3$ , $63x$ , and $54yx$ .

What is this asking? We need to find the biggest expression that divides evenly into $54x^3$ , $63x$ , and $54yx$ . Watch out! Don't forget to consider both the numbers and the variables when finding the GCF!

1. Find the GCF of the coefficients.
2. Find the GCF of the variables.
3. Combine to find the GCF of the expressions.

Let's list out the factors of each coefficient: $54$ : 1, 2, 3, 6, 9, 18, 27, 54 $63$ : 1, 3, 7, 9, 21, 63 $54$ : 1, 2, 3, 6, 9, 18, 27, 54

Looking at the lists, the greatest common factor of 54, 63, and 54 is 9!

The variables in our expressions are $x^3$ , $x$ , and $yx$ .
Notice that all expressions have a factor of $x$ , and only $x$ .
So, our GCF for the variables will definitely include $x$ .

$x^3$ can be written as $x \cdot x \cdot x$ , and $x$ is just $x$ .
Since we're looking for the greatest COMMON factor, we take the smallest power of $x$ present in all terms, which is $x^1$ or just $x$ . $y$ isn't in all the terms, so it won't be in our GCF.

We found that the GCF of the coefficients is 9 and the GCF of the variables is x.
When we put these together, we get $9 \cdot x = 9x$ .

The greatest common factor of $54x^3$ , $63x$ , and $54yx$ is $9x$ .