The HCF of \( \frac{m v^{2}}{t}, \frac{m^{2} v}{t} \) is

To find the highest common factor (HCF) of the expressions \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \), we can follow these steps: 1. **Identify the expressions:** - Let \( A = \frac{m v^{2}}{t} \) - Let \( B = \frac{m^{2} v}{t} \) 2. **Factor out the common terms:** - Both expressions have a common denominator \( t \). - The numerators are \( m v^{2} \) and \( m^{2} v \). 3. **Find the HCF of the numerators:** - The HCF of \( m v^{2} \) and \( m^{2} v \) can be found by taking the lowest power of each variable: - For \( m \): The lowest power is \( m^{1} \). - For \( v \): The lowest power is \( v^{1} \). Therefore, the HCF of the numerators is \( m^{1} v^{1} = mv \). 4. **Combine with the common denominator:** - The HCF of the two expressions is then: \[ \text{HCF} = \frac{mv}{t} \] Thus, the HCF of \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \) is \( \frac{mv}{t} \).