Question
Question
Show Examples
Identify the greatest common factor of 16, w, squared16w
2
and 40, a, to the power 4 , b, cubed, c, squared40a
4
b
3
c
2
.
Answer
Attempt 1 out of 5
Submit Answer
Show Examples
Identify the greatest common factor of 16, w, squared16w
2
and 40, a, to the power 4 , b, cubed, c, squared40a
4
b
3
c
2
.
Answer
Attempt 1 out of 5
Submit Answer
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \( 16w^2 \) and \( 40a^4b^3c^2 \), we will consider both the numerical coefficients and the variables.
### Step 1: Find the GCF of the numerical coefficients (16 and 40)
The prime factorization of the coefficients:
- \( 16 = 2^4 \)
- \( 40 = 2^3 \times 5^1 \)
Now, take the lowest power of each prime factor present in both factorizations:
- For \( 2 \): the minimum between \( 4 \) (from 16) and \( 3 \) (from 40) is \( 3 \).
- \( 5 \) does not appear in \( 16 \), so we won't consider it.
The GCF of \( 16 \) and \( 40 \) is \( 2^3 = 8 \).
### Step 2: Find the GCF of the variables
#### For \( w^2 \) and \( a^4b^3c^2 \):
- The variable \( w \) does not appear in the second expression, so it contributes \( 0 \).
- The variables \( a \), \( b \), and \( c \) contribute \( 0 \) since \( w \) from the first term doesn't match any of the variables in the second expression.
Thus, the GCF for the variables remains as \( 1 \) (essentially no contribution).
### Step 3: Combine the GCFs
Now we combine the GCF of the numerical coefficients and the variables:
\[
\text{GCF} = 8 \cdot 1 = 8
\]
### Final Answer
The greatest common factor of \( 16w^2 \) and \( 40a^4b^3c^2 \) is \( 8 \).
### Step 1: Find the GCF of the numerical coefficients (16 and 40)
The prime factorization of the coefficients:
- \( 16 = 2^4 \)
- \( 40 = 2^3 \times 5^1 \)
Now, take the lowest power of each prime factor present in both factorizations:
- For \( 2 \): the minimum between \( 4 \) (from 16) and \( 3 \) (from 40) is \( 3 \).
- \( 5 \) does not appear in \( 16 \), so we won't consider it.
The GCF of \( 16 \) and \( 40 \) is \( 2^3 = 8 \).
### Step 2: Find the GCF of the variables
#### For \( w^2 \) and \( a^4b^3c^2 \):
- The variable \( w \) does not appear in the second expression, so it contributes \( 0 \).
- The variables \( a \), \( b \), and \( c \) contribute \( 0 \) since \( w \) from the first term doesn't match any of the variables in the second expression.
Thus, the GCF for the variables remains as \( 1 \) (essentially no contribution).
### Step 3: Combine the GCFs
Now we combine the GCF of the numerical coefficients and the variables:
\[
\text{GCF} = 8 \cdot 1 = 8
\]
### Final Answer
The greatest common factor of \( 16w^2 \) and \( 40a^4b^3c^2 \) is \( 8 \).