Solving for the Greatest Common Factor (GCF) of multiple numbers can be a tricky task, especially if the numbers have different variables and exponents. In this post, we will be solving for the GCF of 8m, 36m³, and 12.

To begin, we need to factor each number into its prime factors. For example, 8 can be factored into 2 x 2 x 2, 36 can be factored into 2 x 2 x 3 x 3, and 12 can be factored into 2 x 2 x 3.

Next, we need to identify the common factors among all three numbers. In this case, the common factors are 2 and 2. However, we also need to take into account the variables and their exponents.

Looking at the variables, we can see that all three numbers have an m variable. However, the exponents vary. To find the GCF of the variables, we need to take the smallest exponent of the variable. In this case, m has an exponent of 1 in 8m, an exponent of 3 in 36m³, and no exponent in 12. Therefore, the GCF of the variables is just m.

Now we can combine the GCF of the numbers and the GCF of the variables to find the overall GCF. The GCF of the numbers is 2 x 2 = 4 and the GCF of the variables is m. Therefore, the overall GCF of 8m, 36m³, and 12 is 4m.

In conclusion, solving for the GCF of multiple numbers involves factoring each number into its prime factors, identifying the common factors, and taking into account the variables and their exponents. By following these steps, we were able to find the GCF of 8m, 36m³, and 12, which is 4m.