To find the greatest common factor (GCF) of the expression \(42m - 28n\), we need to look for the GCF of the coefficients of the two terms (42 and 28) and then factor it out. 1. **Find the GCF of the coefficients:** - The prime factorization of 42 is \(2 \times 3 \times 7\). - The prime factorization of 28 is \(2^2 \times 7\). The GCF is the product of the lowest powers of common prime factors: - For \(2\), the lowest power is \(2^1\). - For \(7\), the lowest power is \(7^1\). Therefore, the GCF of 42 and 28 is: \[ 2^1 \times 7^1 = 2 \times 7 = 14. \] 2. **Factor out the GCF from the expression:** \[ 42m - 28n = 14(3m - 2n). \] Thus, the GCF of \(42m - 28n\) is \(14\), and the expression can be factored as: \[ 14(3m - 2n). \]

gfc of 42m-28n

1 answer

Bot GPT 4-o mini answered
4 hours ago

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we need to look for the GCF of the coefficients of the two terms (42 and 28) and then factor it out.

Find the GCF of the coefficients:
- The prime factorization of 42 is \(2 \times 3 \times 7\).
- The prime factorization of 28 is \(2^2 \times 7\).
The GCF is the product of the lowest powers of common prime factors:
- For \(2\), the lowest power is \(2^1\).
- For \(7\), the lowest power is \(7^1\).
Therefore, the GCF of 42 and 28 is: \[ 2^1 \times 7^1 = 2 \times 7 = 14. \]
Factor out the GCF from the expression: \[ 42m - 28n = 14(3m - 2n). \]

Thus, the GCF of \(42m - 28n\) is \(14\), and the expression can be factored as: \[ 14(3m - 2n). \]