Find the greatest common factor (GCF/HCF) of the polynomials $a^2b^3$ and $a^3b^2$.

Given:

Given polynomials are $a^2b^3$ and $a^3b^2$.

To do:

We have to find the greatest common factor of the given polynomials.

Solution:

GCF/HCF:

A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.

The numerical coefficient of $a^2b^3$ is $1$

The numerical coefficient of $a^3b^2$ is $1$

HCF is $1$

The common variables in the given polynomials are $a$ and $b$

The power of $a$ in $a^2b^3$ is $2$

The power of $a$ in $a^3b^2$ is $3$

The power of $b$ in $a^2b^3$ is $3$

The power of $b$ in $a^3b^2$ is $2$

The monomial of common literals with the smallest power is $a^2b^2$

Therefore,

The greatest common factor of the given polynomials is $a^2b^2$.