Question

Find the greatest common factor of each set of monomials.

$6ab,24a{b}^4$

Short answer

The greatest common factor of the given set of monomials is $\mathbf{6}\mathit{a}\mathit{b}$.

Step-by-step solution

Step 1. Find the factorization of 6ab and 24ab4.

Find the factorization of $6ab$and $24a{b}^4$.

$$\begin{gathered} 6ab=2\cdot 3\cdot a\cdot b \\ 24a{b}^4=2\cdot 2\cdot 2\cdot 3\cdot a\cdot b\cdot b\cdot b\cdot b \end{gathered}$$

Step 2. Find the greatest common factor of 6ab and 24ab4.

From the factorization of $6ab$ and $24a{b}^4$, it can be noticed that the greatest common factor of $6ab$ and$24a{b}^4$ is$2\cdot 3\cdot a\cdot b$ or $6ab$.

Therefore, the greatest common factor of the given set of monomials is $6ab$.