Q. 6 QC - Algebra 1

Question

Find the GCF of each pair of monomials.

$\mathbf{12}\mathit{a}\mathit{b}\mathbf{,}\mathbf{18}\mathit{b}$

Step-by-Step Solution

Answer

The GCF of the given pair of monomials is $\mathbf{6}\mathit{b}$.

Step 1. Define greatest common factor.

Greatest common factor is the product of common prime factors of two or more whole numbers. It is a greatest number that is factor of both numbers.

Step 2. Factor each number.

Factor each number and write all powers of variables as products.

$\begin{array}{c}12ab=2\cdot 2\cdot 3\cdot a\cdot b\\ 18b=2\cdot 3\cdot 3\cdot b\end{array}$

Step 3. Find the greatest common factor.

Combine common prime factors to find greatest common factor.

$2\cdot 3\cdot b=6b$ 

Therefore, the GCF of the given pair of monomials is $6b$.