Question

identify the greatest common factor of $40a^{4}cz^{4}$ and $20a^{2}z^{2}$.

Explanation:

Step1: Find GCF of coefficients

The coefficients are 40 and 20. The greatest common factor of 40 and 20 is 20.

Step2: Find GCF of $a$-terms

The $a$-terms are $a^4$ and $a^2$. The GCF uses the lowest exponent: $a^2$.

Step3: Check for common $c$-term

Only $40a^4cz^4$ has a $c$ term, so there is no common $c$ factor.

Step4: Find GCF of $z$-terms

The $z$-terms are $z^4$ and $z^2$. The GCF uses the lowest exponent: $z^2$.

Step5: Multiply all common factors

Multiply the GCFs from each step: $20 \times a^2 \times z^2$

Answer:

$20a^2z^2$