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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 $a^2b^2$.
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