what is the greatest common factor of 45m²n⁴ ; 30mm³​

Answer:To find the greatest common factor (GCF) of the expressions \( 45m^2n^4 \) and \( 30m^3 \), we can break each term down into its prime factors:1. **Factorize the coefficients:** - \( 45 = 3^2 \times 5 \) - \( 30 = 2 \times 3 \times 5 \)2. **Factorize the variables:** - For \( 45m^2n^4 \), the variable factors are \( m^2 \) and \( n^4 \). - For \( 30m^3 \), the variable factor is \( m^3 \).Now, we identify the GCF for the coefficients and the variables:- **Coefficients:** - The common factors of \( 45 \) and \( 30 \) are \( 3 \) and \( 5 \). - The minimum power for \( 3 \) (which appears as \( 3^2 \) in 45 and \( 3^1 \) in 30) is \( 3^1 \). - The minimum power for \( 5 \) (which appears as \( 5^1 \) in both numbers) is \( 5^1 \). - Therefore, the GCF of the coefficients is \( 3^1 \times 5^1 = 15 \).- **Variable factors:** - The common variable factor for \( m \) is \( m \) (minimum of \( m^2 \) and \( m^3 \) is \( m^2 \)). - For \( n \), it appears only in the first expression, so it does not contribute to the GCF.Now, putting it all together:\[\text{GCF} = 15m^2\]Thus, the greatest common factor of \( 45m^2n^4 \) and \( 30m^3 \) is \( 15m^2 \).This message has been generated by Nova - download it for free:https://novaappai.page.link/4p5dWLo4d2penZN86

Answered by sausamarkaldrin | 2024-09-05