Question

What is the greatest common factor of 20y9+5y6?



Responses

5y9
5 y begin power 9 end power

5y6
5 y begin power 6 end power

20y3
20 y cubed

10y9

Answer 1

To find the greatest common factor (GCF) of the expression \(20y^9 + 5y^6\), we can break it down into its components:

1. **Coefficients**: The coefficients of the terms are 20 and 5. The GCF of 20 and 5 is 5.

2. **Variables**: The terms contain the variable \(y\) raised to various powers. The powers are \(y^9\) and \(y^6\). The GCF of \(y^9\) and \(y^6\) is \(y^6\) since we take the lowest power of \(y\).

Now, we combine the GCF of the coefficients and the GCF of the variables:

\[
\text{GCF} = 5y^6
\]

Thus, the greatest common factor of \(20y^9 + 5y^6\) is:

\[
\boxed{5y^6}
\]