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