Question

find the greatest common factor of $8c^2$ and $6n$.

Explanation:

Step1: Factorize 8c²

First, we factorize the coefficient and the variable part of \(8c^{2}\). The prime factorization of 8 is \(2\times2\times2\), and the variable part is \(c\times c\). So, \(8c^{2}=2\times2\times2\times c\times c\).

Step2: Factorize 6n

Next, we factorize \(6n\). The prime factorization of 6 is \(2\times3\), and the variable part is \(n\). So, \(6n = 2\times3\times n\).

Step3: Identify common factors

Now, we look for the common factors between the two factorizations. The only common prime factor is 2, and there are no common variable factors (since \(c^{2}\) and \(n\) are different variables). So, the greatest common factor (GCF) is the product of the common prime factors, which is 2.

Answer:

2