Question

Find the greatest common factor of each set of monomials.

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

Short answer

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

Step-by-step solution

Step 1. Find the factorization of 10ab,30a and 40a2b.

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 10ab,30a and 40a2b.

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 $10a$.