Find the comm a. $$ 16 x y^{2}, 64 x^{2} y $$

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To find the common factors of the given expressions $$ 16xy^2 $$ and $$ 64x^2y $$, we need to identify the greatest common factor (GCF) of the coefficients and the common variables raised to the lowest power.

Let's break down each term:

1. $$ 16xy^2 $$
   - The coefficient is 16.
   - The variable part is $$ xy^2 $$.

2. $$ 64x^2y $$
   - The coefficient is 64.
   - The variable part is $$ x^2y $$.

Now, let's find the GCF of the coefficients (16 and 64) and the GCF of the variable parts ($$ xy^2 $$ and $$ x^2y $$).

For the coefficients:
- The factors of 16 are 1, 2, 4, 8, 16.
- The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
- The greatest common factor of 16 and 64 is 16.

For the variable parts:
- The GCF of $$ xy^2 $$ and $$ x^2y $$ is $$ x $$ because $$ x $$ is the only common variable, and it appears to the lowest power in both terms (once in $$ xy^2 $$ and once in $$ x^2y $$). The $$ y $$ terms are not common, as one has $$ y^2 $$ and the other has $$ y $$.

Therefore, the common factor of the two expressions is $$ 16x $$.

So, the common factor of $$ 16xy^2 $$ and $$ 64x^2y $$ is $$ 16x $$.
The common factor of $$ 16xy^2 $$ and $$ 64x^2y $$ is $$ 16x $$.

Find the comm a. \( 16 x y^{2}, 64 x^{2} y \)

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