Question

Find the greatest common factors of the monomials.

$12m^2{n}^3,70m^{3}n$

Short answer

The greatest common factors of the monomial is $2m^{2}n$.

Step-by-step solution

Step -1 - Apply the concept of   GCF.

In this, simply use the concept of finding the GCF by doing the factors of the number and find the factor which is common and greatest from them.

Step -2 – Find the common factors

Here, the monomials are $12m^2{n}^3,70m^{3}n$

First finding the factors of numbers.

The factor of $12$ is $12=1,2,3,4,6,12$

The factor of $70$ is $70=1,2,5,35,70$

Again, find the factors of variables

The factor of $m^2{n}^3$ is $m^2{n}^3=m\times m\times n\times n\times n$

The factor of $m^{3}n$ is $m^{3}n=m\times m\times m\times n$

Step -3 – Finding the GCF 

Now, the common factor among the numbers are $2$.

the common factor among the variables are $m\times m\times n$

So, the greatest common factor is $2m^{2}n$.