Identify the greatest common factor of 18, b18b and 6, b6b.

Answer 1

To find the greatest common factor (GCF) of the terms given, we first consider the numerical coefficients and then any variables present.

1. Numerical Coefficients:

   • The coefficients in the terms are 18, 18, 6, and 6.
   • To find the GCF of these numbers, we first list their factors:
     • Factors of 18: 1, 2, 3, 6, 9, 18
     • Factors of 6: 1, 2, 3, 6

   Now, the common factors are 1, 2, 3, and 6. The greatest common factor among these is 6.

2. Variables:

   • The terms include \( b \) in both \( 18b \) and \( 6b \). We find the lowest power of \( b \) present in both terms. Here, both terms contain \( b^1 \).

Now we can combine the GCF of the numerical coefficients and the variable factor:

The greatest common factor of the terms \( 18b, 18b, 6b, 6b \) is: \[ \text{GCF} = 6b \]

Thus, the final answer is 6b.