Find the GCF (greatest common factor) of the following terms.
{25xy2^,75y^2}
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.
25 =25
75 = 25*3
so
GCF of 25 and 75 is 25
Apologies for the mistake.
You're correct, the GCF of 25 and 75 is indeed 25.
So
therefore, the GCF of 25xy^2 and 75y^2 is 25 * y^2, NOT 5 y^2.
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.
To find the greatest common factor (GCF) of 25xy^2 and 75y^2, we need to determine the largest term that can divide both of these terms evenly. Here's how you can find the GCF:
Step 1: Prime Factorization
Write down the prime factorization of each term.
25xy^2 = 5 * 5 * x * y * y
75y^2 = 5 * 5 * 3 * y * y
Step 2: Identify Common Factors
Look for common factors in the prime factorizations. These are the factors that appear in both terms.
Both terms have 5 * 5 * y * y as common factors.
Step 3: Determine GCF
To find the GCF, multiply all the common factors together:
GCF = 5 * 5 * y * y
GCF = 25y^2
Therefore, the GCF of 25xy^2 and 75y^2 is 25y^2.