Find the GCF for the list. \[ 245 a^{5} b^{4} c^{2}, 175 a^{6} b \] The GCF is $\square$.
Solution
Step 1 ：Given the expressions \(245 a^{5} b^{4} c^{2}\) and \(175 a^{6} b\), we are asked to find the Greatest Common Factor (GCF).
Step 2 ：The GCF of two or more numbers is the largest number that divides evenly into each of the numbers. In this case, we are asked to find the GCF of two algebraic expressions. To find the GCF of algebraic expressions, we need to find the common factors of the coefficients and the common factors of the variables.
Step 3 ：For the coefficients, we need to find the GCF of 245 and 175. The GCF of 245 and 175 is 35.
Step 4 ：For the variables, we need to find the common factors of \(a^{5}\) and \(a^{6}\), \(b^{4}\) and \(b\), and \(c^{2}\) and no \(c\) in the second term.
Step 5 ：The GCF of the variable \(a\) is \(a^{5}\), the GCF of the variable \(b\) is \(b\), and the GCF of the variable \(c\) is \(c^{0}\), which is 1.
Step 6 ：Therefore, the GCF of the two expressions is \(35a^{5}b\).
Step 7 ：Final Answer: The GCF is \(\boxed{35a^{5}b}\).
