Q. 8 QC - Algebra 1

Question

Find the GCF of each pair of monomials.

$\mathbf{60}{\mathit{r}}^2\mathbf{,}\mathbf{45}{\mathit{r}}^3$

Step-by-Step Solution

Answer

The GCF of the given pair of monomials is $\mathbf{15}{\mathit{r}}^2$.

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.

$\begin{array}{c}60r^2=2\cdot 2\cdot 3\cdot 5\cdot r\cdot r\\ 45r^3=3\cdot 3\cdot 5\cdot r\cdot r\cdot r\end{array}$

Step 3. Find the greatest common factor.

Combine common prime factors to find greatest common factor.

$3\cdot 5\cdot r\cdot r=15r^2$ 

Therefore, the GCF of the given pair of monomials is $15r^2$.