Question

What would be the GCF of the following two terms? 50x^5y^2z^2 and 125x^3y^3z

Answer 1

Answer: x^3y^2z

Explanation:

To find the GCF (Greatest Common Factor) of the terms 50x^5y^2z^2 and 125x^3y^3z, we need to identify the largest factor that is common to both terms.

First, we can break down each term into its prime factors:

50x^5y^2z^2 = 2 * 5^2 * x^5 * y^2 * z^2

125x^3y^3z = 5^3 * x^3 * y^3 * z

Now we can identify the common factors by looking at the prime factors that are common to both terms:

x^3

y^2

z

The GCF is the product of these common factors:

GCF = x^3 * y^2 * z = x^3y^2z

Therefore, the GCF of 50x^5y^2z^2 and 125x^3y^3z is x^3y^2z.

Answer 2

For the coefficients, the prime factorization of 50 is 2 x 5 x 5, and the prime factorization of 125 is 5 x 5 x 5. The common factors are 5 x 5 = 25.

For the variables, we can find the lowest exponent of each variable that appears in both terms.

The variable x appears in both terms, with exponents of 5 and 3. The lowest exponent is 3.

The variable y appears in both terms, with exponents of 2 and 3. The lowest exponent is 2.

The variable z appears in both terms, with exponents of 2 and 1. The lowest exponent is 1.

Therefore, the GCF of 50x^5y^2z^2 and 125x^3y^3z is 25x^3y^2z.