Question: Find the greatest common factor of these three expressions. 42v, 70v^2, and 28v^4

Find the greatest common factor of these three expressions. 42v, 70v^2, and 28v^4

Solution

To find the greatest common factor (GCF) of the three expressions \(42v\), \(70v^2\), and \(28v^4\), we need to consider both the numerical coefficients and the variable parts. First, find the GCF of the numerical coefficients 42, 70, and 28. 1. List the prime factors: - \(42 = 2 \times 3 \times 7\) - \(70 = 2 \times 5 \times 7\) - \(28 = 2 \times 2 \times 7\) 2. Identify the common prime factors: - The common prime factor is \(2 \times 7 = 14\). Next, find the GCF of the variable part \(v\), \(v^2\), and \(v^4\). 3. Identify the lowest power of \(v\): - The lowest power is \(v\). Combine the GCFs of the numerical and variable parts: 4. The GCF of the expressions \(42v\), \(70v^2\), and \(28v^4\) is: \[ 14v \]