Q18. - Algebra 1

Question

Find the greatest common factor of each set of monomials.

$10ab,30a,40a^{2}b$

Step-by-Step Solution

Answer

The greatest common factor of the given set of monomials is $10a$.

Step 1. Find the factorization of 10 a b , 30 a and 40 a 2 b .

Find the factorization of $10ab$,$30a$ and $40a^{2}b$.

$$\begin{gathered} 10ab=2\cdot 5\cdot a\cdot b \\ 30a=2\cdot 3\cdot 5\cdot a \\ 40a^{2}b=2\cdot 2\cdot 2\cdot 5\cdot a\cdot a\cdot b \end{gathered}$$

Step 2. Find the greatest common factor of 10 a b , 30 a and 40 a 2 b .

From the factorization of $10ab,30a$ and $40a^{2}b$, it can be noticed that the greatest common factor of $10ab,30a$, and $40a^{2}b$ is $2\cdot 5\cdot a$ or $10a$.

Therefore, the greatest common factor of the given set of monomials is $10a$.