Q9. - Algebra 1

Question

Find the GCF of each pair of monomials.

$12xy,16x^{2}y$

Step-by-Step Solution

Answer

The GCF of the given pair of monomials is $4xy$.

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.

 $$\begin{gathered} 12xy=2\cdot 2\cdot 3\cdot x\cdot y \\ 16x^{2}y=2\cdot 2\cdot 2\cdot 2\cdot x\cdot x\cdot y \end{gathered}$$

Step 3. Find the greatest common factor.

Combine common prime factors to find greatest common factor.

 

$2\cdot 2\cdot x\cdot y=4xy$

 

Therefore, the GCF of the given pair of monomials is $4xy$.