Question

Find the greatest common factor

6x^2y^4+18x^3y^5-12x^5y^3

Answer 1

6x^2y^3

Explanation:

6x^2y^4+18x^3y^5-12x^5y^3

Lets check the coefficients first:-

6, 18, 12 - The GCF is 6.

x terms:- x^2, x^3 and x^5 . The GCF is x^2.

y terms:- y^4, y^5 and y^3. The GCF is y^3.

Answer 2

6x^2y^3

Explanation:

6x^2y^4+18x^3y^5-12x^5y^3

Lets break each term into prime factors

6x^2y^4 =3*2*x*x*y*y*y*y

18x^3y^5 = 9*2^3y^5 = 3*3*2*x*x*x*y*y*y*y*y

12x^5y^3 = 4*3x^5y^3 = 2*2*3*x*x*x*x*x*y*y*y

Each has one 2, one 3, two x's and three y's

So the greatest common factor is

2*3*x*x*y*y*y

6x^2y^3