Question

Find the greatest common factor.'
8m^3,6m^2

Answer 1

To find the greatest common factor (GCF) of the expressions \(8m^3\) and \(6m^2\), we can follow these steps:

1. **Factor the coefficients**:
- The coefficients are 8 and 6.
- The prime factorization of 8 is \(2^3\).
- The prime factorization of 6 is \(2^1 \cdot 3^1\).
- The GCF of the coefficients is the product of the lowest powers of all prime factors:
- For \(2\), the minimum power is \(1\) (from \(6\)).
- For \(3\), it is \(0\) (since \(8\) does not have \(3\)).
- Thus, the GCF of the coefficients \(8\) and \(6\) is \(2^1 = 2\).

2. **Factor the variable parts**:
- For \(m^3\) and \(m^2\), the GCF is \(m\) raised to the lowest power, which is \(m^2\).

3. **Combine the GCF components**:
- Combine the GCF of the coefficients and the variables:
\[
\text{GCF} = 2m^2
\]

Therefore, the greatest common factor of \(8m^3\) and \(6m^2\) is \(\boxed{2m^2}\).