Find the GCF of 42m−28n .(1 point)
Responses
84
84
7
7
14
14
2
Responses
84
84
7
7
14
14
2
Answers
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Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the expression \(42m - 28n\), we first look for the GCF of the numerical coefficients.
The coefficients are 42 and 28.
1. **Find the prime factorization of 42**:
\(42 = 2 \times 3 \times 7\)
2. **Find the prime factorization of 28**:
\(28 = 2^2 \times 7\)
Now, we identify the common prime factors:
- The number 2 appears in both factorizations (the lowest power is \(2^1\)).
- The number 7 also appears in both factorizations.
Next, we take the product of the lowest powers of the common prime factors:
\[
GCF = 2^1 \times 7^1 = 2 \times 7 = 14
\]
Now, putting it into the expression, we can factor out the GCF:
\[
42m - 28n = 14(3m - 2n)
\]
So, the GCF of \(42m - 28n\) is \(14\).
The correct response is **14**.
The coefficients are 42 and 28.
1. **Find the prime factorization of 42**:
\(42 = 2 \times 3 \times 7\)
2. **Find the prime factorization of 28**:
\(28 = 2^2 \times 7\)
Now, we identify the common prime factors:
- The number 2 appears in both factorizations (the lowest power is \(2^1\)).
- The number 7 also appears in both factorizations.
Next, we take the product of the lowest powers of the common prime factors:
\[
GCF = 2^1 \times 7^1 = 2 \times 7 = 14
\]
Now, putting it into the expression, we can factor out the GCF:
\[
42m - 28n = 14(3m - 2n)
\]
So, the GCF of \(42m - 28n\) is \(14\).
The correct response is **14**.
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