Question

Find the greatest common divisor of:
$7x^{2}y{z}^4,21x^2{y}^5{z}^3$

• A. $7x^{2}y{z}^3$
• B. $2x^{2}y{z}^3$
• C. $7x^{3}y{z}^3$
• D. None of these

Answer 1

The correct option is A $7x^{2}y{z}^3$

We first factorize the given monomials $7x^{2}y{z}^4$ and $21x^2{y}^5{z}^3$ as shown below:

$7x^{2}y{z}^4=7\times x\times x\times y\times z\times z\times z\times z21x^2{y}^5{z}^3=7\times 3\times x\times x\times y\times y\times y\times y\times y\times z\times z\times z$

The common factors of $7x^{2}y{z}^4$ and $21x^2{y}^5{z}^3$ are $7,x^2,y$ and $z^3$, therefore, the GCF is:

$7\times x\times x\times y\times z\times z\times z=7x^{2}y{z}^3$

Hence, the greatest common divisor of $7x^{2}y{z}^4$ and $21x^2{y}^5{z}^3$ is $7x^{2}y{z}^3$.