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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 $7x$.
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