Question

Find the GCF of each pair of monomials60p and 12

Answer 1

By definition, a monomial is a polynomial that has one term.

In this case you have these monomials:

$\begin{gathered} 60p \\ 12 \end{gathered}$

In order to find the Greatest Common Factor (GCF) of this pair of monomials (which is also known as Greatest Common Divisor), you can apply the steps shown below:

Step 1. You need to descompose each monomial into its prime factors, as following:

$\begin{gathered} 60p=2\cdot2\cdot3\cdot5\cdot p=2^2\cdot3\cdot5\cdot p \\ 12=2\cdot2\cdot3=2^2\cdot3 \end{gathered}$

Step 2. Now you must choose the common factors with the lowest exponents and then you must multiply them. The product will be the Greatest Common Factor. Then:

$GCF=2^2\cdot3=4\cdot3=12$

The answer is:

$GCF=12$