what is the GCF (greatest common factor) of the following terms.
{90,30xy2,60xy}
To find the GCF of the terms 90, 30xy^2, and 60xy, we need to find the highest common factor that divides all three terms.
First, let's break down each term into its prime factors:
90 = 2 * 3^2 * 5
30xy^2 = 2 * 3 * 5 * x * y^2
60xy = 2^2 * 3 * 5 * x * y
Now, we look for the highest powers of each prime factor that appear in all three terms. The factors 2, 3, 5, x, and y all appear in each term, but the highest power of each factor is:
2^1 * 3^1 * 5^1 * x^1 * y^1
Thus, the GCF of 90, 30xy^2, and 60xy is 2 * 3 * 5 * x * y, which can be simplified to 30xy.