Question

find the greatest common factor of 20y^4 and 15y^2.

Explanation:

Step1: Factorize coefficients

Factorize 20 and 15. $20 = 2\times2\times5$, $15=3\times5$. The greatest - common factor of 20 and 15 is 5.

Step2: Analyze variable part

For the variable part $y^{4}$ and $y^{2}$, using the rule of exponents for GCF of powers of the same base $a^{m}$ and $a^{n}$ ($m\geq n$), the GCF is $a^{n}$. So the GCF of $y^{4}$ and $y^{2}$ is $y^{2}$.

Step3: Combine results

The GCF of $20y^{4}$ and $15y^{2}$ is the product of the GCF of the coefficients and the GCF of the variable parts, which is $5y^{2}$.

Answer:

$5y^{2}$