Find the greatest common factor (GCF/HCF) of the polynomial $7x, 21x^2$ and $14xy^2$.

Given:

Given polynomials are $7x, 21x^2$ and $14xy^2$.

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 $7x$ is $7$

The numerical coefficient of $21x^2$ is $21$

The numerical coefficient of $14xy^2$ is $14$

This implies,

$7=7\times1$

$21=3\times7$

$14=2\times7$

HCF of $7, 21$ and $14$ is $7$

The common variables in the given polynomials are $x$ and $y$

The power of $x$ in $7x$ is $1$

The power of $x$ in $21x^2$ is $2$

The power of $x$ in $14xy^2$ is $1$

The power of $y$ in $7x$ is $0$

The power of $y$ in $21x^2$ is $0$

The power of $y$ in $14xy^2$ is $2$

The monomial of common literals with the smallest power is $x$

Therefore,

The greatest common factor of the given polynomials is $7x$.