Question

What are the common factors of $3x^{3}y,5x{y}^2,\text{and}15xy$ ?

• A. $x,y,xy,x{y}^2,x^{3}y$
• B. $x,y,xy,x{y}^2,$
• C. $x,y,xy,$
• D. $xy,x{y}^2,x^{3}y$

Answer 1

The correct option is C $x,y,xy,$

On factorising the given monomials we get:
$3x^{3}y=3\times x\times x\times x\times y$
$5x{y}^2=5\times x\times y\times y$
$15xy=3\times 5\times x\times y$
The common irreducible factors in all three expressions are $x$ and $y$.
So, the common factors of the given expressions are $x,y,\text{and}xy$.