Question: Find the greatest common factor of \(15a^4\) and \(9y^3\).

Find the greatest common factor of \(15a^4\) and \(9y^3\).

Solution

To find the greatest common factor (GCF) of \(15a^4\) and \(9y^3\), we follow these steps: 1. Identify the factors of each coefficient: - The factors of 15 are 1, 3, 5, and 15. - The factors of 9 are 1, 3, and 9. The greatest common factor of 15 and 9 is 3. 2. Identify the common variables: - \(15a^4\) has the variable part \(a^4\). - \(9y^3\) has the variable part \(y^3\). Since there are no common variables, the greatest common factor for the variables is 1. 3. Combine the results: The GCF of the numerical parts is 3, and there is no common variable factor. Therefore, the GCF of \(15a^4\) and \(9y^3\) is \(3\).