Question: Find the greatest common factor of these three expressions. 8v^4, 20v^3, and 12v^5

Find the greatest common factor of these three expressions. 8v^4, 20v^3, and 12v^5

Solution

To find the greatest common factor (GCF) of the expressions \(8v^4\), \(20v^3\), and \(12v^5\), follow these steps: First, find the GCF of the numerical coefficients: The coefficients are 8, 20, and 12. Find the factors of each: - Factors of 8: \(1, 2, 4, 8\) - Factors of 20: \(1, 2, 4, 5, 10, 20\) - Factors of 12: \(1, 2, 3, 4, 6, 12\) The common factors are \(1, 2, 4\). The greatest is 4. Next, find the GCF of the variable part \(v^4\), \(v^3\), and \(v^5\): - The lowest power of \(v\) is \(v^3\). Combine both results: The GCF is \(4v^3\). Therefore, the greatest common factor of the expressions \(8v^4\), \(20v^3\), and \(12v^5\) is \(4v^3\).