The GCF is xy
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xy
I do the coefficients first. The GCF of 10 and 15 is 5. I tackle the variables next. The GCF of x2y and x3y2 is x2y I put it all together. The GCF of 15x2y and 10x3y2 is 5x2y.
The GCF of 27 x^2 y^3 and 46 x^2 y is xy^2. 27 and 46 are coprime.
3 * 3 * 5 * x * y * y = 45xy2
To find the greatest common factor of x^2y and xy^2, we need to determine the highest power of each variable that is common to both terms. In this case, the common factors are x and y. The highest power of x that is common to both terms is x^1, and the highest power of y that is common to both terms is y^1. Therefore, the greatest common factor of x^2y and xy^2 is xy.