Question

find the greatest common factor of these two expressions. $30v^{2}u^{4}x^{5}$ and $22v^{3}u^{4}$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 30 and 22.
Factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$
Factors of 22: $1, 2, 11, 22$
Greatest common factor is $2$.

Step2: Find GCF of $v$-terms

The $v$-terms are $v^2$ and $v^3$.
Use the lower exponent: $v^2$.

Step3: Find GCF of $u$-terms

The $u$-terms are $u^4$ and $u^4$.
Use the lower exponent: $u^4$.

Step4: Find GCF of $x$-terms

The $x$-terms are $x^5$ and $x^0$ (since the second expression has no $x$).
Use the lower exponent: $x^0=1$, so no $x$ term in GCF.

Step5: Multiply all GCF parts

Multiply the results from steps 1-4: $2 \times v^2 \times u^4$

Answer:

$2u^4v^2$