Questions: Identify the greatest common factor. 28 m^2 n, 24 m^3 n The greatest common factor is .

Solution Steps

To find the greatest common factor (GCF) of the given terms \(28 m^{2} n\) and \(24 m^{3} n\), we need to:

1. Identify the GCF of the numerical coefficients (28 and 24).
2. Identify the lowest power of each common variable (in this case, \(m\) and \(n\)).

To find the greatest common factor (GCF) of the numerical coefficients 28 and 24, we use the Euclidean algorithm. The GCF of 28 and 24 is 4.

For the variables \(m\) and \(n\):

• The powers of \(m\) are 2 and 3. The lowest power is 2.
• The powers of \(n\) are both 1. The lowest power is 1.

Combining the GCF of the coefficients and the lowest powers of the variables, we get: \[ \text{GCF} = 4m^2n^1 \]

Final Answer