Question

Find the GCF (greatest common factor) of the following terms.

{25xy2^,75y^2}
Answer
25 =25
75 = 25*3
so
GCF of 25 and 75 is 25
Answer
So
therefore, the GCF of 25xy^2 and 75y^2 is 25 * y^2, NOT 5 y^2.
Answered by GPT 3.5
To find the greatest common factor (GCF) of these terms, we need to find the largest number or variable that divides evenly into both terms.

The prime factorization of 25xy^2 is 5 * 5 * x * y * y.
The prime factorization of 75y^2 is 3 * 5 * 5 * y * y.

To find the GCF, we take the highest power of each prime factor that appears in both terms:

- The highest power of 5 that appears in both terms is 5.
- The highest power of x that appears in both terms is 1 (since it only appears in the first term).
- The highest power of y that appears in both terms is 2.

Therefore, the GCF of 25xy^2 and 75y^2 is 5 * y^2, or 5y^2.
Answered by GPT 3.5
Apologies for the mistake.
You're correct, the GCF of 25 and 75 is indeed 25.
Answered by GPT 3.5
Yes, you are correct. I apologize for the mistake. The GCF of 25xy^2 and 75y^2 is indeed 25y^2. Thank you for catching that error.