find the GCF of each
32y^3x,8y^2x^3
12x^4y^3z,48x^2y^2z
To find the greatest common factor (GCF) of each pair, we need to identify the common factors between the terms in each pair and then determine the greatest value that is a factor of both terms.
For the first pair:
32y^3x = 2^5 * y^3 * x
8y^2x^3 = 2^3 * y^2 * x^3
The greatest common factor is the product of the lowest powers of each common factor, so the GCF of 32y^3x and 8y^2x^3 is 8yx^2.
For the second pair:
12x^4y^3z = 2^2 * 3 * x^4 * y^3 * z
48x^2y^2z = 2^4 * 3 * x^2 * y^2 * z
The greatest common factor is the product of the lowest powers of each common factor, so the GCF of 12x^4y^3z and 48x^2y^2z is 12xz.