The GCF is 3.
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2x2 + 6xy = 2x (x + 3y)
Since 3y^2 is a factor of 18y^2, it is automatically the GCF.
The GCF of 12y^3 and 15y^2 is 3y^2
Since 3y2 can evenly divide 24y3, 3y2 must be the greatest common factor, since the greatest common factor cannot be larger than the smaller of the two numbers. But, we can also look at a factorization of both numbers. We can tell that 3y2 = 3 x y2. We can tell that 24y3 = 3 x 8 x y3 = 3 x 23 x y2 x y. These numbers have in common 3 and y2, so 3y2 is the greatest common factor.
To factor 4x + 12y, you first need to find the greatest common factor of the coefficients 4 and 12, which is 4. Then, you factor out the common factor from the terms: 4(x + 3y). This is the factored form of 4x + 12y.