Find the greatest common factor between 16x^2 and 48x^3. Show your work.
To find the greatest common factor between 16x^2 and 48x^3, we need to factorize both of the expressions.
For 16x^2:
16 = 2^4
x^2 = x * x
So, 16x^2 can be written as 2^4 * x * x.
For 48x^3:
48 = 2^4 * 3
x^3 = x * x * x
So, 48x^3 can be written as 2^4 * 3 * x * x * x.
Now, we need to find the common factors between these two expressions. The common factors are 2^4 and x. The highest power of x is x^2, so we can write the common factors as 2^4 * x^2.
Therefore, the greatest common factor between 16x^2 and 48x^3 is 2^4 * x^2, which simplifies to 16x^2.