Question

Find the greatest common factor of the monomials.

$32y^2,6x^{2}y$

Short answer

The greatest common factor is $2y$.

Step-by-step solution

Step-1 – Define monomials

A monomial is an expression that has a single term, with variables and a coefficient. For example, $2xy$ is a monomial since it is a single term, has two variables, and one coefficient.

Step-2 – Define greatest common factor

A common factor is a whole number that is a factor of two or more nonzero whole numbers. The greatest of the common factors is the greatest common factor (GCF). The same concept is applicable to the monomials.

Step-3 – Factor the monomials

The factors of $6x^{2}y$are: $6x^{2}y=2\times 3\times y\times x\times x$.

The factors of $32y^2$are: localid="1651713996662" $32y^2=2\times 2\times 2\times 2\times 2\times y\times y$

Since $2\times y$is common between the two monomials, therefore, the greatest common factor is 2y.