Question

Find the greatest common factor of 28y⁽⁵⁾w⁽⁴⁾ and 8y⁽⁸⁾w⁽⁷⁾u⁽²⁾ ?

Answer 1

To find the greatest common factor (GCF) of 28y⁵w⁴ and 8y⁸w⁷u², determine the highest power of each variable that appears in both terms. The GCF of the powers of 'y' is 5, the GCF of the powers of 'w' is 4, and the GCF of the powers of 'u' is 0. Therefore, the GCF is 5y⁵w⁴.

Step-by-step explanation:

To find the greatest common factor (GCF) of 28y⁵w⁴ and 8y⁸w⁷u², we need to determine the highest power of each variable that appears in both terms.

First, let's look at the powers of 'y'. The highest power of 'y' in 28y⁵w⁴ is 5, and the highest power of 'y' in 8y⁸w⁷u² is 8. Therefore, the GCF of the powers of 'y' is 5.

Next, let's consider the powers of 'w'. The highest power of 'w' in 28y⁵w⁴ is 4, and the highest power of 'w' in 8y⁸w⁷u² is 7. Thus, the GCF of the powers of 'w' is 4.

Since there are no 'u' terms in the first expression and the highest power of 'u' in the second expression is 2, the GCF of the powers of 'u' is 0.

Now, we can put together the powers of the common variables: y⁵w⁴. Therefore, the greatest common factor of 28y⁵w⁴ and 8y⁸w⁷u² is 5y⁵w⁴.