Show the prime factorisation of the following numbers:

$8712$

_____ is a factor of every term.

$1-{\left(x-y\right)}^2=\left(1+x-y\right)\times$_____

$x^{2}yz+x{y}^{2}z+xy{z}^2=$_____

$p\left(x-2\right)+2q(2-x)=$_____

Find the greatest common factor of the given monomials.

$3m$, $6n$

Find the greatest common factor of the given monomials.

$ax$, $-5ab$

If the greatest common factor of the given monomials $18x^7$, $-9x^3$ is $k{x}^3$, find the value of $k$.

Find the greatest common factor of the given monomials.

$10xy$, $15x^2{y}^3$