Find the GCF (greatest common factor) of the following terms. {3xy^2,2x^2,3x^2y^2}
wrong again
the GCF is just x
Apologies for the mistake in my previous response. You are correct.
Looking at the terms 3xy^2, 2x^2, and 3x^2y^2, the variable x appears in each term with a minimum exponent of 1. Therefore, the GCF is x.
To find the greatest common factor (GCF) of the terms {3xy^2, 2x^2, 3x^2y^2}, we need to find the common factors of these terms and determine the largest one.
Step 1: Break down each term into its prime factors.
- 3xy^2: This term has three factors—3, x, and y^2.
- 2x^2: This term has two factors—2 and x^2.
- 3x^2y^2: This term has four factors—3, x^2, y^2.
Step 2: Identify the common factors of the terms.
The common factors among the terms are 1, x, and x^2.
Step 3: Determine the largest common factor.
The largest common factor is x^2.
Therefore, the GCF of the terms {3xy^2, 2x^2, 3x^2y^2} is x^2.
To find the greatest common factor (GCF) of these terms, we look for the highest power of each variable that appears in all the terms.
The prime factorization of each term is:
- 3xy^2 = 3 * x * y * y
- 2x^2 = 2 * x * x
- 3x^2y^2 = 3 * x * x * y * y
Looking at the prime factorization, we can see that the common factors are 3, x, and y^2.
Therefore, the GCF of {3xy^2, 2x^2, 3x^2y^2} is 3xy^2.